WorldCat Identities

Galatius, Søren 1976-

Works: 15 works in 24 publications in 1 language and 114 library holdings
Genres: Conference proceedings 
Roles: Editor, Thesis advisor, Author
Classifications: QA612.14, 514.2
Publication Timeline
Publications about  Søren Galatius Publications about Søren Galatius
Publications by  Søren Galatius Publications by Søren Galatius
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 88 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
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
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
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
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
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
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
Filtered floer and symplectic homology via Gromov-Witten 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 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
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
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
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
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
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
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])
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  Kids General Special  
Audience level: 0.82 (from 0.47 for Divisibili ... to 0.92 for Algebraic ...)
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English (24)