# Galatius, Søren 1976-

Overview
Works: 23 works in 36 publications in 1 language and 192 library holdings Conference papers and proceedings Editor, Author, Thesis advisor QA612.14, 514.2
Publication Timeline
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Most widely held works by Søren Galatius
Algebraic topology : applications and new directions : Stanford Symposium on Algebraic Topology: Applications and New Directions, July 23--27, 2012, Stanford University, Stanford, CA by Stanford Symposium on Algebraic Topology : Applications and New Directions( Book )

5 editions published in 2014 in English and held by 111 WorldCat member libraries worldwide

Impact of microvascular alterations in heart failure : effect of cardiac transplantation and ACE inhibition by Søren Galatius( Book )

4 editions published in 2001 in English and held by 9 WorldCat member libraries worldwide

Divisibility of the stable Miller-Morita-Mumford class by Søren Galatius( Book )

4 editions published in 2005 in English and held by 7 WorldCat member libraries worldwide

Mod p homology of the stable mapping class group by Søren Galatius( Book )

4 editions published in 2002 in English and held by 7 WorldCat member libraries worldwide

Characteristic classes of surface bundles( Book )

1 edition published in 2004 in English and held by 1 WorldCat member library worldwide

The topology of spaces of J-holomorphic maps to CP2 by Jeremy Kenneth Miller( )

1 edition published in 2012 in English and held by 1 WorldCat member library worldwide

In [Seg79], Graeme Segal proved that the space of holomorphic maps from a Riemann surface to a complex projective space is homology equivalent to the corresponding continuous mapping space through a range of dimensions increasing with degree. I will address if a similar result holds when other almost complex structures are put on projective space. For any compatible almost complex structure J on CP^2, I prove that the inclusion map from the space of J-holomorphic maps to the space of continuous maps induces a homology surjection through a range of dimensions tending to infinity with degree. The proof involves comparing the scanning map of topological chiral homology ([Sal01], [Lur09], [And10]) with gluing of J-holomorphic curves ([MS94], [Sik03])
Non-Abelian Lefschetz hyperplane theorems by Daniel Litt( )

1 edition published in 2015 in English and held by 1 WorldCat member library worldwide

Let X be a smooth variety over the complex numbers, and let D be an ample divisor in X. For which spaces Y does every map from D to Y extend uniquely to a map X to Y? Our main result, proved via positive characteristic methods, is the following: if dim(X)> 2, Y is smooth, the cotangent bundle of Y is nef, and dim(Y) <dim(D), every such map extends. Taking Y to be the classifying space of a finite group BG, the moduli space of pointed curves M_g, n, the moduli space of principally polarized Abelian varieties A_g, certain period domains, and various other moduli spaces, one obtains many new and classical Lefschetz hyperplane theorems. We also prove many other such extension theorems, and develop general techniques for recognizing spaces Y for which these sorts of Lefschetz theorems hold
The string topology of holomorphic curves in BU(n) by Sam Nolen( )

1 edition published in 2016 in English and held by 1 WorldCat member library worldwide

In this thesis we compute the string topology algebra structure on the homology of a stabilized version of the space of holomorphic maps from 1-dimensional complex projective space to a complex Grassmannian. This generalizes a computation of Kallel and Salvatore
Duality and linear approximations in Hochschild homology, K-theory, and string topology by Cary Malkiewich( )

1 edition published in 2014 in English and held by 1 WorldCat member library worldwide

This thesis encompasses at least three separate but related projects. The first project is a treatment of twisted Poincare duality for manifolds with coefficients in spectra, and is included as an appendix. The second project investigates the map from the stabilization of the gauge group of a certain principal bundle over a manifold M to the Cohen-Jones string topology spectrum of M. This map is a linear approximation in the sense of Goodwillie and Weiss's embedding calculus. The third project is an ongoing and open-ended exploration of contravariant forms of algebraic K-theory of spaces, with a focus on topological Hochschild homology
Relations among characteristic classes of manifold bundles by Ilya Grigoriev( )

1 edition published in 2013 in English and held by 1 WorldCat member library worldwide

We study a generalization of the tautological subring of the cohomology of the moduli space of Riemann surfaces to manifold bundles. The infinitely many "generalized Miller-Morita-Mumford classes" determine a map R from a free polynomial algebra to the cohomology of the classifying space of manifold bundles. In the case when M is the connected sum of g copies of the product of spheres (S^d times S^d), with d odd, we find numerous polynomials in the kernel of the map R and show that the image of R is a finitely generated ring. Some of the elements in the kernel do not depend on d. Our results contrast with the fact that the map R is an isomorphism in a range of cohomological degrees that grows linearly with g. This is known from theorems of Madsen-Weiss and Harer for the case of surfaces (d=1) and from the recent work of Soren Galatius and Oscar Randal-Williams in higher dimensions. For surfaces, the image of the map R coincides with the classical tautological ring, as introduced by Mumford
Some finiteness results for groups of automorphisms of manifolds by Alexander Kupers( )

1 edition published in 2016 in English and held by 1 WorldCat member library worldwide

We prove that in dimensions not equal to 4,5,7 the homology and homotopy groups of the topological group of diffeomorphisms of a disk fixing the boundary are finitely generated in each degree. The proof uses homological stability, embedding calculus and the arithmeticity of mapping class groups. From this we deduce similar results for the homeomorphisms of R^n and various types of automorphisms of 2-connected manifolds
Some results on K-theory, topological Hochschild homology, and parameterized spectra by Jonathan Alfred Campbell( )

1 edition published in 2013 in English and held by 1 WorldCat member library worldwide

This thesis comprises three separate papers. The first proves a duality result relating the topological Hochschild homology of a ring spectrum to the Spanier-Whitehead dual of the topological Hochschild homology of the Koszul dual ring spectrum. The second, proves an additivity result for the transfer A-theory of infinity topoi, as introduced by Barwick. The third presents partial results of joint work with John Lind. In the full joint paper we create a machine which has as input 2-Vector bundles and as output parameterized ku-modules
Moduli spaces of pseudo-holomorphic disks and floer theory of cleanly intersecting immersed lagrangians by Yin Kwan Chan( )

1 edition published in 2010 in English and held by 1 WorldCat member library worldwide

In this thesis we investigate moduli spaces of pseudo-holomorphic disks with Lagrangian boundary conditions, in which the Lagrangians are immersed with clean self-intersections. We then discuss the compactification of these moduli spaces, and show that under specific assumptions, the moduli spaces can be oriented. Finally, we use these moduli spaces to construct and compute Lagrangian Floer cohomology for sphere and orientation covers of the real projective space embedded as a Lagrangian submanifold of the complex projective space
Stable moduli of flat manifold bundles by Sam Nariman( )

1 edition published in 2015 in English and held by 1 WorldCat member library worldwide

Flat manifold bundles (i.e. manifold bundles with foliations transverse to the fibers) are classified by homotopy classes of maps to the classifying space of diffeomorphisms made discrete. In my thesis, I studied the homology of the classifying spaces of discrete diffeomorphisms for certain type of manifolds including surfaces, higher dimensional analogue of surfaces and disks with punctures. I established homological stability of discrete surface diffeomorphisms and discrete symplectic diffeomorphisms which was conjectured by Morita. To study the stable homology of these family of groups, I described an infinite loop space related to the Haefliger space whose homology is the same as group homology of discrete surface diffeomorphisms in the stable range which is the analogous of the Madsen-Weiss theorem for discrete surface diffeomorphisms. Similar theorems were proved for punctured 2-dimensional disk and higher dimensional analogue of surfaces. I utilized these new techniques of studying discrete diffeomorphism groups to obtain interesting applications to the characteristic classes of flat surface bundles and foliated bordism groups of codimension 2 foliations
String topology and twisted K-theory by Anssi Sebastian Lahtinen( )

1 edition published in 2010 in English and held by 1 WorldCat member library worldwide

The mathematics in this thesis is motivated by the desire to connect the twisted equivariant K-theory of a compact Lie group G to the string topology of its classifying space BG. The thesis consists of two parts. In the first part, we prove a generalization of the Atiyah--Segal completion theorem to twisted K-theory, a result which Kriz, Westerland and Levin have subsequently used to connect the twisted equivariant K-groups of G to the Gruher--Salvatore string topology of BG. In the second part, we present work towards the construction of a conjectural family of field theories which, on one hand, are closely related to Freed, Hopkins and Teleman's field theories featuring the twisted equivariant K-theory of G, and which on the other hand contain the Chataur--Menichi string topology of BG as a special case. The main result of the second part is the construction of the field-theory operation associated with a fixed cobordism
String topology and the based loop space by Eric James Malm( )

1 edition published in 2010 in English and held by 1 WorldCat member library worldwide

We relate the Batalin-Vilkovisky (BV) algebra structure of the string topology of a manifold to the homological algebra of the singular chains of the based loop space of that manifold, showing that its Hochschild cohomology carries a BV algebra structure isomorphic to that of string topology. Furthermore, this structure is compatible with the usual cup product and Lie bracket on Hochschild cohomology. This isomorphism arises from a derived form of Poincare duality using modules over the based loop space as local coefficient systems. This derived Poincare duality also comes from a form of fibrewise Atiyah duality on the level of fibrewise spectra, and we use this perspective to connect the algebraic constructions to the Chas-Sullivan loop product
The moduli space of real curves and a Z/2-equivariant Madsen-Weiss theorem by Nisan Alexander Stiennon( )

1 edition published in 2013 in English and held by 1 WorldCat member library worldwide

Galatius, Madsen, Tillmann, and Weiss proved that the classifying space of the category of 2-cobordisms is equivalent to the loopspace of a particular Thom spectrum. We show that this is in fact a Z/2-equivariant equivalence, where we equip all spaces with a Z/2-action which is motivated by complex conjugation of complex curves. In order to do this, we prove an equivariant delooping theorem which shows that grouplike topological monoids with Z/2-action are Z/2-equivalent to loopspaces. Furthermore, we motivate our choice of Z/2-action by showing that it determines a Z/2-space BDiff_g whose fixed points classify real 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 pluri-subharmonic 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 Bourgeois-Eckholm-Eliashberg (\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
A duality theorem for deligne-mumford stacks with respect to Morava K-theory by Man Chuen Cheng( )

1 edition published in 2011 in English and held by 1 WorldCat member library worldwide

In [7] Greenlees and Sadofsky used a transfer map to show that the classifying spaces of finite groups are self-dual with respect to Morava K-theory K(n). By regarding these classifying spaces as the homotopy types of certain differentiable stacks, their construction can be viewed as a stack version of Spanier-Whitehead type construction. From this point of view, we will extend their results and prove a K(n)-version of Poincare duality for Deligne-Mumford stacks. A few examples of stacks defined by finite groups and moduli stack of Riemann surfaces will be discussed at the end
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 pseudo-holomorphic 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" pseudo-holomorphic curves. We introduce the notion of an implicit atlas on a moduli space, which is (roughly) a convenient system of local finite-dimensional reductions. We present a general intrinsic strategy for constructing a canonical implicit atlas on any moduli space of pseudo-holomorphic 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). Sheaf-theoretic tools play an important role in setting up our functorial algebraic "VFC package". We illustrate the methods we introduce by giving definitions of Gromov--Witten 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, Hofer--Salamon, Ono, Liu--Tian, Ruan, and Fukaya--Ono) is a well-known corollary of this calculation. We give a construction of contact homology in the sense of Eliashberg--Givental--Hofer. Specifically, we use implicit atlases to construct coherent virtual fundamental cycles on the relevant compactified moduli spaces of holomorphic curves

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Alternative Names
Søren Galatius dänischer Mathematiker

Søren Galatius Danish mathematician

Søren Galatius wiskundige uit Denemarken

Languages
English (33)