WorldCat Identities

Galatius, Søren 1976-

Works: 18 works in 30 publications in 1 language and 149 library holdings
Genres: Conference proceedings 
Roles: Author, Thesis advisor, Editor
Classifications: QA612.14, 514.2
Publication Timeline
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 )

4 editions published in 2014 in English and held by 97 WorldCat member libraries worldwide

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

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

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
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
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
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
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
Equivariant algebraic k-theory of products of motivic circles by Tracy Leah Nance( )

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

Fix an algebraically closed field k of characteristic zero. We describe a method which produces deloopings of K'(k) in the Gm(k)-direction via a homotopy limit over pth power maps, and examine the outcome of analogous constructions in an equivariant setting. These constructions provide a technique for studying actions of finite groups on motivic spheres which cannot be described by a usual smash product of Gm's with group action
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])
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
Characteristic classes of surface bundles( Book )

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

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
Filtered floer and symplectic homology via Gromov-Witten theory by Lus 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 Gromov--Witten invariants, and some additional Morse-theoretic 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 homotopy-theoretic view of Bott-Taubes integrals and knot spaces by Robin Michael John Koytcheff( )

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

We construct cohomology classes in the space of knots by considering a bundle over this space and "integrating along the fiber'' classes coming from the cohomology of configuration spaces using a Pontrjagin-Thom construction. The bundle we consider is essentially the one considered by Bott and Taubes, who integrated differential forms along the fiber to get knot invariants. By doing this "integration'' homotopy-theoretically, we are able to produce integral cohomology classes. Inspired by results of Budney and Cohen, we study how this integration is compatible with homology operations on the space of long knots. In particular we derive a product formula for evaluations of cohomology classes on homology classes, with respect to connect-sum of knots. We then adapt the construction to be compatible with tools coming from the Goodwillie-Weiss embedding calculus, in particular Sinha's cosimplicial model for the space of knots
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
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
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Audience level: 0.72 (from 0.65 for Algebraic ... to 0.96 for Impact of ...)

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Alternative Names
Sren Galatius dnischer Mathematiker

English (30)