Galatius, Søren 1976Overview
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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 2327, 2012, Stanford University, Stanford, CA
by Stanford Symposium on Algebraic Topology: Applications and New Directions
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4 editions published in 2014 in English and held by 88 WorldCat member libraries worldwide
Mod p homology of the stable mapping class group
by Søren Galatius
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4 editions published in 2002 in English and held by 7 WorldCat member libraries worldwide
Divisibility of the stable MillerMoritaMumford class
by Søren Galatius
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4 editions published in 2005 in English and held by 7 WorldCat member libraries worldwide
String topology and twisted Ktheory
by Anssi Sebastian Lahtinen
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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 Ktheory 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 AtiyahSegal completion theorem to twisted Ktheory, a result which Kriz, Westerland and Levin have subsequently used to connect the twisted equivariant Kgroups of G to the GruherSalvatore 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 Ktheory of G, and which on the other hand contain the ChataurMenichi string topology of BG as a special case. The main result of the second part is the construction of the fieldtheory operation associated with a fixed cobordism
Duality and linear approximations in Hochschild homology, Ktheory, and string topology
by Cary Malkiewich
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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 CohenJones 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 openended exploration of contravariant forms of algebraic Ktheory of spaces, with a focus on topological Hochschild homology
Moduli spaces of pseudoholomorphic disks and floer theory of cleanly intersecting immersed lagrangians
by Yin Kwan Chan
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1 edition published in 2010 in English and held by 1 WorldCat member library worldwide In this thesis we investigate moduli spaces of pseudoholomorphic disks with Lagrangian boundary conditions, in which the Lagrangians are immersed with clean selfintersections. 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
A duality theorem for delignemumford stacks with respect to Morava Ktheory
by Man Chuen Cheng
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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 selfdual with respect to Morava Ktheory 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 SpanierWhitehead type construction. From this point of view, we will extend their results and prove a K(n)version of Poincare duality for DeligneMumford stacks. A few examples of stacks defined by finite groups and moduli stack of Riemann surfaces will be discussed at the end
Equivariant algebraic ktheory of products of motivic circles
by Tracy Leah Nance
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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
Filtered floer and symplectic homology via GromovWitten theory
by Luís Miguel Pereira De Matos Geraldes Diogo
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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
Some results on Ktheory, topological Hochschild homology, and parameterized spectra
by Jonathan Alfred Campbell
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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 SpanierWhitehead dual of the topological Hochschild homology of the Koszul dual ring spectrum. The second, proves an additivity result for the transfer Atheory 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 2Vector bundles and as output parameterized kumodules
The moduli space of real curves and a Z/2equivariant MadsenWeiss theorem
by Nisan Alexander Stiennon
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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 2cobordisms is equivalent to the loopspace of a particular Thom spectrum. We show that this is in fact a Z/2equivariant equivalence, where we equip all spaces with a Z/2action 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/2action are Z/2equivalent to loopspaces. Furthermore, we motivate our choice of Z/2action by showing that it determines a Z/2space BDiff_g whose fixed points classify real curves
A homotopytheoretic view of BottTaubes integrals and knot spaces
by Robin Michael John Koytcheff
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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 PontrjaginThom 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'' homotopytheoretically, 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 connectsum of knots. We then adapt the construction to be compatible with tools coming from the GoodwillieWeiss embedding calculus, in particular Sinha's cosimplicial model for the space of knots
String topology and the based loop space
by Eric James Malm
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1 edition published in 2010 in English and held by 1 WorldCat member library worldwide We relate the BatalinVilkovisky (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 ChasSullivan loop product
Relations among characteristic classes of manifold bundles
by Ilya Grigoriev
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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 MillerMoritaMumford 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 MadsenWeiss and Harer for the case of surfaces (d=1) and from the recent work of Soren Galatius and Oscar RandalWilliams in higher dimensions. For surfaces, the image of the map R coincides with the classical tautological ring, as introduced by Mumford
The topology of spaces of Jholomorphic maps to CP2
by Jeremy Kenneth Miller
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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 Jholomorphic 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 Jholomorphic curves ([MS94], [Sik03]) more
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