Eliashberg, Y. 1946
Overview
Works:  32 works in 119 publications in 2 languages and 2,059 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Author, Editor, Thesis advisor, Other 
Classifications:  QA665, 516.36 
Publication Timeline
.
Most widely held works by
Y Eliashberg
Introduction to the hprinciple by
Y Eliashberg(
Book
)
12 editions published in 2002 in English and held by 246 WorldCat member libraries worldwide
In differential geometry and topology one often deals with systems of partial differential equations, as well as partial differential inequalities, that have infinitely many solutions whatever boundary conditions are imposed. It was discovered in the fifties that the solvability of differential relations (i.e. equations and inequalities) of this kind can often be reduced to a problem of a purely homotopytheoretic nature. One says in this case that the corresponding differential relation satisfies the $h$principle. Two famous examples of the $h$principle, the NashKuiper $C^1$isometric embedding theory in Riemannian geometry and the SmaleHirsch immersion theory in differential topology, were later transformed by Gromov into powerful general methods for establishing the $h$principle. The authors cover two main methods for proving the $h$principle: holonomic approximation and convex integration. The reader will find that, with a few notable exceptions, most instances of the $h$principle can be treated by the methods considered here. A special emphasis in the book is made on applications to symplectic and contact geometry. Gromov's famous book ``Partial Differential Relations'', which is devoted to the same subject, is an encyclopedia of the $h$principle, written for experts, while the present book is the first broadly accessible exposition of the theory and its applications. The book would be an excellent text for a graduate course on geometric methods for solving partial differential equations and inequalities. Geometers, topologists and analysts will also find much value in this very readable exposition of an important and remarkable topic
12 editions published in 2002 in English and held by 246 WorldCat member libraries worldwide
In differential geometry and topology one often deals with systems of partial differential equations, as well as partial differential inequalities, that have infinitely many solutions whatever boundary conditions are imposed. It was discovered in the fifties that the solvability of differential relations (i.e. equations and inequalities) of this kind can often be reduced to a problem of a purely homotopytheoretic nature. One says in this case that the corresponding differential relation satisfies the $h$principle. Two famous examples of the $h$principle, the NashKuiper $C^1$isometric embedding theory in Riemannian geometry and the SmaleHirsch immersion theory in differential topology, were later transformed by Gromov into powerful general methods for establishing the $h$principle. The authors cover two main methods for proving the $h$principle: holonomic approximation and convex integration. The reader will find that, with a few notable exceptions, most instances of the $h$principle can be treated by the methods considered here. A special emphasis in the book is made on applications to symplectic and contact geometry. Gromov's famous book ``Partial Differential Relations'', which is devoted to the same subject, is an encyclopedia of the $h$principle, written for experts, while the present book is the first broadly accessible exposition of the theory and its applications. The book would be an excellent text for a graduate course on geometric methods for solving partial differential equations and inequalities. Geometers, topologists and analysts will also find much value in this very readable exposition of an important and remarkable topic
Symplectic geometry and topology by
Y Eliashberg(
Book
)
15 editions published between 1999 and 2008 in English and held by 245 WorldCat member libraries worldwide
15 editions published between 1999 and 2008 in English and held by 245 WorldCat member libraries worldwide
Confoliations by
Y Eliashberg(
Book
)
12 editions published between 1997 and 1998 in English and held by 242 WorldCat member libraries worldwide
12 editions published between 1997 and 1998 in English and held by 242 WorldCat member libraries worldwide
From Stein to Weinstein and back : symplectic geometry of affine complex manifolds by
Kai Cieliebak(
Book
)
9 editions published in 2012 in English and held by 233 WorldCat member libraries worldwide
9 editions published in 2012 in English and held by 233 WorldCat member libraries worldwide
Northern California symplectic geometry seminar by Northern California Symplectic Geometry Seminar(
Book
)
11 editions published in 1999 in English and held by 192 WorldCat member libraries worldwide
11 editions published in 1999 in English and held by 192 WorldCat member libraries worldwide
Different faces of geometry by
S. K Donaldson(
Book
)
11 editions published in 2004 in English and held by 158 WorldCat member libraries worldwide
Different Faces of Geometry  edited by the world renowned geometers S. Donaldson, Ya. Eliashberg, and M. Gromov  presents the current state, new results, original ideas and open questions from the following important topics in modern geometry: Amoebas and Tropical Geometry Convex Geometry and Asymptotic Geometric Analysis Differential Topology of 4Manifolds 3Dimensional Contact Geometry Floer Homology and LowDimensional Topology Khler Geometry Lagrangian and Special Lagrangian Submanifolds Refined SeibergWitten Invariants. These apparently diverse topics have a common feature in that they are all areas of exciting current activity. The Editors have attracted an impressive array of leading specialists to author chapters for this volume: G. Mikhalkin (USACanadaRussia), V.D. Milman (Israel) and A.A. Giannopoulos (Greece), C. LeBrun (USA), Ko Honda (USA), P. Ozsvth (USA) and Z. Szab (USA), C. Simpson (France), D. Joyce (UK) and P. Seidel (USA), and S. Bauer (Germany). "One can distinguish various themes running through the different contributions. There is some emphasis on invariants defined by elliptic equations and their applications in lowdimensional topology, symplectic and contact geometry (Bauer, Seidel, Ozsvth and Szab). These ideas enter, more tangentially, in the articles of Joyce, Honda and LeBrun. Here and elsewhere, as well as explaining the rapid advances that have been made, the articles convey a wonderful sense of the vast areas lying beyond our current understanding. Simpson's article emphasizes the need for interesting new constructions (in that case of Khler and algebraic manifolds), a point which is also made by Bauer in the context of 4manifolds and the "11/8 conjecture". LeBrun's article gives another perspective on 4manifold theory, via Riemannian geometry, and the challenging open questions involving the geometry of even "wellknown" 4manifolds. There are also striking contrasts between the articles. The authors have taken different approaches: for example, the thoughtful essay of Simpson, the new research results of LeBrun and the thorough expositions with homework problems of Honda. One can also ponder the differences in the style of mathematics. In the articles of Honda, Giannopoulos and Milman, and Mikhalkin, the "geometry" is present in a very vivid and tangible way; combining respectively with topology, analysis and algebra. The papers of Bauer and Seidel, on the other hand, makes the point that algebraic and algebrotopological abstraction (triangulated categories, spectra) can play an important role in very unexpected ways in concrete geometric problems."The Preface by the Editors
11 editions published in 2004 in English and held by 158 WorldCat member libraries worldwide
Different Faces of Geometry  edited by the world renowned geometers S. Donaldson, Ya. Eliashberg, and M. Gromov  presents the current state, new results, original ideas and open questions from the following important topics in modern geometry: Amoebas and Tropical Geometry Convex Geometry and Asymptotic Geometric Analysis Differential Topology of 4Manifolds 3Dimensional Contact Geometry Floer Homology and LowDimensional Topology Khler Geometry Lagrangian and Special Lagrangian Submanifolds Refined SeibergWitten Invariants. These apparently diverse topics have a common feature in that they are all areas of exciting current activity. The Editors have attracted an impressive array of leading specialists to author chapters for this volume: G. Mikhalkin (USACanadaRussia), V.D. Milman (Israel) and A.A. Giannopoulos (Greece), C. LeBrun (USA), Ko Honda (USA), P. Ozsvth (USA) and Z. Szab (USA), C. Simpson (France), D. Joyce (UK) and P. Seidel (USA), and S. Bauer (Germany). "One can distinguish various themes running through the different contributions. There is some emphasis on invariants defined by elliptic equations and their applications in lowdimensional topology, symplectic and contact geometry (Bauer, Seidel, Ozsvth and Szab). These ideas enter, more tangentially, in the articles of Joyce, Honda and LeBrun. Here and elsewhere, as well as explaining the rapid advances that have been made, the articles convey a wonderful sense of the vast areas lying beyond our current understanding. Simpson's article emphasizes the need for interesting new constructions (in that case of Khler and algebraic manifolds), a point which is also made by Bauer in the context of 4manifolds and the "11/8 conjecture". LeBrun's article gives another perspective on 4manifold theory, via Riemannian geometry, and the challenging open questions involving the geometry of even "wellknown" 4manifolds. There are also striking contrasts between the articles. The authors have taken different approaches: for example, the thoughtful essay of Simpson, the new research results of LeBrun and the thorough expositions with homework problems of Honda. One can also ponder the differences in the style of mathematics. In the articles of Honda, Giannopoulos and Milman, and Mikhalkin, the "geometry" is present in a very vivid and tangible way; combining respectively with topology, analysis and algebra. The papers of Bauer and Seidel, on the other hand, makes the point that algebraic and algebrotopological abstraction (triangulated categories, spectra) can play an important role in very unexpected ways in concrete geometric problems."The Preface by the Editors
Symplectic and contact topology : interactions and perspectives by
Y Eliashberg(
Book
)
8 editions published in 2003 in English and Undetermined and held by 144 WorldCat member libraries worldwide
8 editions published in 2003 in English and Undetermined and held by 144 WorldCat member libraries worldwide
Symplectic, Poisson, and noncommutative geometry by Algebra and Topology (Conference) Symplectic and Poisson Geometry in Interaction with Analysis(
Book
)
5 editions published in 2014 in English and Undetermined and held by 125 WorldCat member libraries worldwide
5 editions published in 2014 in English and Undetermined and held by 125 WorldCat member libraries worldwide
Geometries in interaction : GAFA special issue in honor of Mikhail Gromov by
Y Eliashberg(
Book
)
11 editions published between 1995 and 2003 in English and held by 77 WorldCat member libraries worldwide
Reprint from GAFA, Vol. 5 (1995), No. 2. Enlarged by a short biography of Mikhail Gromov and a list of publications. In the last decades of the XX century tremendous progress has been achieved in geometry. The discovery of deep interrelations between geometry and other fields including algebra, analysis and topology has pushed it into the mainstream of modern mathematics. This Special Issue of Geometric And Functional Analysis (GAFA) in honour of Mikhail Gromov contains 14 papers which give a wide panorama of recent fundamental developments in modern geometry and its related subjects. CONTRIBUTORS: J. Bourgain, J. Cheeger, J. Cogdell, A. Connes, Y. Eliashberg, H. Hofer, F. Lalonde, W. Luo, G. Margulis, D. McDuff, H. Moscovici, G. Mostow, S. Novikov, G. Perelman, I. PiatetskiShapiro, G. Pisier, X. Rong, Z. Rudnick, D. Salamon, P. Sarnak, R. Schoen, M. Shubin, K. Wysocki, and E. Zehnder. The book is a collection of important results and an enduring source of new ideas for researchers and students in a broad spectrum of directions related to all aspects of Geometry and its applications to Functional Analysis, PDE, Analytic Number Theory and Physics
11 editions published between 1995 and 2003 in English and held by 77 WorldCat member libraries worldwide
Reprint from GAFA, Vol. 5 (1995), No. 2. Enlarged by a short biography of Mikhail Gromov and a list of publications. In the last decades of the XX century tremendous progress has been achieved in geometry. The discovery of deep interrelations between geometry and other fields including algebra, analysis and topology has pushed it into the mainstream of modern mathematics. This Special Issue of Geometric And Functional Analysis (GAFA) in honour of Mikhail Gromov contains 14 papers which give a wide panorama of recent fundamental developments in modern geometry and its related subjects. CONTRIBUTORS: J. Bourgain, J. Cheeger, J. Cogdell, A. Connes, Y. Eliashberg, H. Hofer, F. Lalonde, W. Luo, G. Margulis, D. McDuff, H. Moscovici, G. Mostow, S. Novikov, G. Perelman, I. PiatetskiShapiro, G. Pisier, X. Rong, Z. Rudnick, D. Salamon, P. Sarnak, R. Schoen, M. Shubin, K. Wysocki, and E. Zehnder. The book is a collection of important results and an enduring source of new ideas for researchers and students in a broad spectrum of directions related to all aspects of Geometry and its applications to Functional Analysis, PDE, Analytic Number Theory and Physics
Confoliations by
Y Eliashberg(
Book
)
1 edition published in 1998 in English and held by 7 WorldCat member libraries worldwide
1 edition published in 1998 in English and held by 7 WorldCat member libraries worldwide
Different Faces of Geometry by
S. K Donaldson(
)
2 editions published in 2004 in English and held by 5 WorldCat member libraries worldwide
2 editions published in 2004 in English and held by 5 WorldCat member libraries worldwide
Topological characterization of Stein manifolds of dimension>2 by
Y Eliashberg(
Book
)
1 edition published in 1989 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1989 in English and held by 2 WorldCat member libraries worldwide
Beʻolam hahafikhot by
Yaʻaḳov Eliʼasberg(
Book
)
1 edition published in 1965 in Hebrew and held by 2 WorldCat member libraries worldwide
1 edition published in 1965 in Hebrew and held by 2 WorldCat member libraries worldwide
Three examples from symplectic topology by
Y Eliashberg(
Visual
)
2 editions published in 2002 in English and held by 2 WorldCat member libraries worldwide
2 editions published in 2002 in English and held by 2 WorldCat member libraries worldwide
Filtered floer and symplectic homology via GromovWitten theory by Luís Miguel Pereira De Matos Geraldes Diogo(
)
1 edition published in 2012 in English and held by 1 WorldCat member library worldwide
We describe a procedure for computing Floer and symplectic homology groups, with action filtration and algebraic operations, in a class of examples. Namely, we consider closed monotone symplectic manifolds with smooth symplectic divisors, Poincaré dual to a positive multiple of the symplectic form. We express the Floer homology of the manifold and the symplectic homology of the complement of the divisor, for a special class of Hamiltonians, in terms of absolute and relative GromovWitten invariants, and some additional Morsetheoretic information. As an application, we compute the symplectic homology rings of cotangent bundles of spheres, and compare our results with an earlier computation in string topology
1 edition published in 2012 in English and held by 1 WorldCat member library worldwide
We describe a procedure for computing Floer and symplectic homology groups, with action filtration and algebraic operations, in a class of examples. Namely, we consider closed monotone symplectic manifolds with smooth symplectic divisors, Poincaré dual to a positive multiple of the symplectic form. We express the Floer homology of the manifold and the symplectic homology of the complement of the divisor, for a special class of Hamiltonians, in terms of absolute and relative GromovWitten invariants, and some additional Morsetheoretic information. As an application, we compute the symplectic homology rings of cotangent bundles of spheres, and compare our results with an earlier computation in string topology
A new construction of virtual fundamental cycles in symplectic geometry by John Vincent Pardon(
)
1 edition published in 2015 in English and held by 1 WorldCat member library worldwide
We develop techniques for defining and working with virtual fundamental cycles on moduli spaces of pseudoholomorphic curves which are not necessarily cut out transversally. Such techniques have the potential for applications as foundations for invariants in symplectic topology arising from "counting" pseudoholomorphic curves. We introduce the notion of an implicit atlas on a moduli space, which is (roughly) a convenient system of local finitedimensional reductions. We present a general intrinsic strategy for constructing a canonical implicit atlas on any moduli space of pseudoholomorphic curves. The main technical step in applying this strategy in any particular setting is to prove appropriate gluing theorems. We require only topological gluing theorems, that is, smoothness of the transition maps between gluing charts need not be addressed. Our approach to virtual fundamental cycles is algebraic rather than geometric (in particular, we do not use perturbation). Sheaftheoretic tools play an important role in setting up our functorial algebraic "VFC package". We illustrate the methods we introduce by giving definitions of GromovWitten invariants and Hamiltonian Floer homology over $\QQ$ for general symplectic manifolds. Our framework generalizes to the $S^1$equivariant setting, and we use $S^1$localization to calculate Hamiltonian Floer homology. The Arnold conjecture (as treated by Floer, HoferSalamon, Ono, LiuTian, Ruan, and FukayaOno) is a wellknown corollary of this calculation. We give a construction of contact homology in the sense of EliashbergGiventalHofer. Specifically, we use implicit atlases to construct coherent virtual fundamental cycles on the relevant compactified moduli spaces of holomorphic curves
1 edition published in 2015 in English and held by 1 WorldCat member library worldwide
We develop techniques for defining and working with virtual fundamental cycles on moduli spaces of pseudoholomorphic curves which are not necessarily cut out transversally. Such techniques have the potential for applications as foundations for invariants in symplectic topology arising from "counting" pseudoholomorphic curves. We introduce the notion of an implicit atlas on a moduli space, which is (roughly) a convenient system of local finitedimensional reductions. We present a general intrinsic strategy for constructing a canonical implicit atlas on any moduli space of pseudoholomorphic curves. The main technical step in applying this strategy in any particular setting is to prove appropriate gluing theorems. We require only topological gluing theorems, that is, smoothness of the transition maps between gluing charts need not be addressed. Our approach to virtual fundamental cycles is algebraic rather than geometric (in particular, we do not use perturbation). Sheaftheoretic tools play an important role in setting up our functorial algebraic "VFC package". We illustrate the methods we introduce by giving definitions of GromovWitten invariants and Hamiltonian Floer homology over $\QQ$ for general symplectic manifolds. Our framework generalizes to the $S^1$equivariant setting, and we use $S^1$localization to calculate Hamiltonian Floer homology. The Arnold conjecture (as treated by Floer, HoferSalamon, Ono, LiuTian, Ruan, and FukayaOno) is a wellknown corollary of this calculation. We give a construction of contact homology in the sense of EliashbergGiventalHofer. Specifically, we use implicit atlases to construct coherent virtual fundamental cycles on the relevant compactified moduli spaces of holomorphic curves
On symplectic homology of the complement of a positive normal crossing divisor in a projective variety by Khoa Lu Nguyen(
)
1 edition published in 2015 in English and held by 1 WorldCat member library worldwide
This dissertation studies how symplectic homology of the complement of the smooth zero set $D$ of a section of a positive line bundle $\cL$ over a projective variety $(X, J)$ changes as $D$ degenerates to a normal crossing divisor $D_{\mbox{sing}}$ with two smooth connected components. By analyzing the plurisubharmonic functions obtained from a metric on $\cL$, we show that the change in the Weinstein structure of the complement is characterized by handle removals along the unstable submanifolds of critical points in a small neighborhood of the set of singular points of $D_{\mbox{sing}}.$ Parallel to work by BourgeoisEckholmEliashberg (\cite{BEE}), we construct a chain complex from the removed unstable submanifolds such that its homology completes the Viterbo transfer map in a long exact sequence. The effect of divisor degeneration on symplectic homology of the complement is then essentially reflected by the $A_\infty$ structure of a collection of Lagrangian spheres on $D$, which are the boundary at infinity of the removed unstable submanifolds
1 edition published in 2015 in English and held by 1 WorldCat member library worldwide
This dissertation studies how symplectic homology of the complement of the smooth zero set $D$ of a section of a positive line bundle $\cL$ over a projective variety $(X, J)$ changes as $D$ degenerates to a normal crossing divisor $D_{\mbox{sing}}$ with two smooth connected components. By analyzing the plurisubharmonic functions obtained from a metric on $\cL$, we show that the change in the Weinstein structure of the complement is characterized by handle removals along the unstable submanifolds of critical points in a small neighborhood of the set of singular points of $D_{\mbox{sing}}.$ Parallel to work by BourgeoisEckholmEliashberg (\cite{BEE}), we construct a chain complex from the removed unstable submanifolds such that its homology completes the Viterbo transfer map in a long exact sequence. The effect of divisor degeneration on symplectic homology of the complement is then essentially reflected by the $A_\infty$ structure of a collection of Lagrangian spheres on $D$, which are the boundary at infinity of the removed unstable submanifolds
Northern California Sympletic Seminar(
Book
)
1 edition published in 1999 in English and held by 1 WorldCat member library worldwide
1 edition published in 1999 in English and held by 1 WorldCat member library worldwide
Three examples from symplectic topology by
Y Eliashberg(
Visual
)
1 edition published in 2002 in English and held by 1 WorldCat member library worldwide
1 edition published in 2002 in English and held by 1 WorldCat member library worldwide
Orientability of moduli spaces and open GromovWitten invariants by Penka Vasileva Georgieva(
)
1 edition published in 2011 in English and held by 1 WorldCat member library worldwide
We show that the local system of orientations on the moduli space of Jholomorphic maps from a bordered Riemann surface is isomorphic to the pullback of a local system defined on the product of the Lagrangian and its free loop space. The latter is defined using only the first and second StiefelWhitney classes of the Lagrangian. In the presence of an antisymplectic involution, whose fixed locus is a relatively spin Lagrangian, we define open GromovWitten type invariants in genus zero
1 edition published in 2011 in English and held by 1 WorldCat member library worldwide
We show that the local system of orientations on the moduli space of Jholomorphic maps from a bordered Riemann surface is isomorphic to the pullback of a local system defined on the product of the Lagrangian and its free loop space. The latter is defined using only the first and second StiefelWhitney classes of the Lagrangian. In the presence of an antisymplectic involution, whose fixed locus is a relatively spin Lagrangian, we define open GromovWitten type invariants in genus zero
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Related Identities
 Gromov, Mikhael 1943 Honoree Dedicatee Editor
 Donaldson, S. K. Author Editor
 Mishachev, N. (Nikolai M.) 1952
 Thurston, William P. 19462012
 Cieliebak, Kai 1966 Author
 Traynor, Lisa (Lisa M.) 1964 Editor
 Rațiu, Tudor S. Editor
 Weinstein, Alan 1943 Editor
 Fuks, D. B. Editor
 Khesin, Boris A. Editor
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Associated Subjects
Differentiable manifolds Differential equations, Partial Differential equationsNumerical solutions Differential topology Europe, Eastern Foliations (Mathematics) Functional analysis Geometry Geometry, Differential Global analysis (Mathematics) Jews, Polish Jews, Russian Mathematical analysis Mathematics Noncommutative differential geometry Poisson manifolds Poland Soviet Union Stein manifolds Symplectic and contact topology Symplectic geometry Symplectic groups Symplectic manifolds Threefolds (Algebraic geometry) Threemanifolds (Topology) Topology Zionism
Alternative Names
Eliasberg, Jakov M. 1946
Ēlîʾašberg, Y. 1946
Eliasberg, Y. M. 1946
Eli'asberg, Ya'aqov 1946
Eliasberg, Yaqoov 1946
Eliasberg, Yaqoov M. 1946
Eliashberg, Y.
Eliashberg, Y. 1946
Eliashberg, Ya.
Eliashberg, Ya 1946
Eliashberg, Yakov.
Eliashberg, Yakov 1946
Eliashberg, Yakov M.
Eliashberg, Yakov M. 1946
Eliashberg, Yasha 1946
Jakov Eliasjberg
Jakow Matwejewitsch Eliaschberg russischer Mathematiker
Yakov Eliashberg mathématicien russe
Yakov Eliashberg Russisch wiskundige
Элиашберг, Яков Матвеевич
یاکوو الیاشبرگ
ヤコフ・エリアシュバーグ
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