116 citations · 1.7k across the 92 of their papers we have counts for
33 papers · 1 filter
A Fixed Point Decomposition of Twisted Equivariant K-Theory
Tom Dove, Thomas Schick, Mario Velásquez
We present a decomposition of rational twisted -equivariant K-theory, a finite group, into cyclic group equivariant K-theory groups of fixed point spaces. This generalises t…
Conormal homology of manifolds with corners
Thomas Schick, Mario Velasquez
Given a manifold with corners , we associates to it the corner structure simplicial complex . Its reduced K-homology is isomorphic to the K-theory of the -algebra $\ma…
Positive Scalar Curvature due to the Cokernel of the Classifying Map
Thomas Schick, Vito Felice Zenobi
This paper contributes to the classification of positive scalar curvature metrics up to bordism and up to concordance. Let be a closed spin manifold of dimension which…
The Gromov-Lawson codimension 2 obstruction to positive scalar curvature and the C*-index
Yosuke Kubota, Thomas Schick
Gromov and Lawson developed a codimension 2 index obstruction to positive scalar curvature for a closed spin manifold M, later refined by Hanke, Pape and Schick. Kubota has shown t…
Mapping analytic surgery to homology, higher rho numbers and metrics of positive scalar curvature
Paolo Piazza, Thomas Schick, Vito Felice Zenobi
Let be a f.g. discrete group and let be a Galois -covering of a smooth closed manifold . Let be the analytic structure group, appearing in t…
On an Index Theorem of Chang, Weinberger and Yu
Thomas Schick, Mehran Seyedhosseini
In this paper we prove a strengthening of a theorem of Chang, Weinberger and Yu on obstructions to the existence of positive scalar curvature metrics on compact manifolds with boun…
C*-Algebraic Higher Signatures and an Invariance Theorem in Codimension Two
Nigel Higson, Thomas Schick, Zhizhang Xie
We revisit the construction of signature classes in C*-algebra K-theory, and develop a variation that allows us to prove equality of signature classes in some situations involving…
Index Theory and the Baum-Connes conjecture
Thomas Schick
These notes are based on lectures on index theory, topology, and operator algebras at the "School on High Dimensional Manifold Theory" at the ICTP in Trieste, and at the Seminari d…
Codimension two index obstructions to positive scalar curvature
Bernhard Hanke, Daniel Pape, Thomas Schick
We derive a general obstruction to the existence of Riemannian metrics of positive scalar curvature on closed spin manifolds in terms of hypersurfaces of codimension two. The proof…
The surgery exact sequence, K-theory and the signature operator
Paolo Piazza, Thomas Schick
The main result of this paper is a new and direct proof of the natural transformation from the surgery exact sequence in topology to the analytic K-theory sequence of Higson and Ro…
Large scale index of multi-partitioned manifolds
Thomas Schick, Mostafa Esfahani Zadeh
Let M be a complete n-dimensional Riemannian spin manifold, partitioned by q two-sided hypersurfaces which have a compact transverse intersection N and which in addition satisfy a…
Rho-classes, index theory and Stolz' positive scalar curvature sequence
Paolo Piazza, Thomas Schick
In this paper, we study the space of metrics of positive scalar curvature using methods from coarse geometry. Given a closed spin manifold M with fundamental group G, Stephan Stolz…
C*-Algebra approach to the index theory of boundary value problems
Severino Melo, Elmar Schrohe, Thomas Schick
Boutet de Monvel's calculus provides a pseudodifferential framework which encompasses the classical differential boundary value problems. In an extension of the concept of Lopatins…
Families index for Boutet de Monvel operators
Severino Melo, Elmar Schrohe, Thomas Schick
We define the analytical and the topological indices for continuous families of operators in the C*-closure of the Boutet de Monvel algebra. Using techniques of C*-algebra K-theory…
Differential K-theory. A survey
Ulrich Bunke, Thomas Schick
Generalized differential cohomology theories, in particular differential K-theory (often called "smooth K-theory"), are becoming an important tool in differential geometry and in m…
Corrigendum: Uniqueness of smooth extensions of generalized cohomology theories
Ulrich Bunke, Thomas Schick
The proof of Theorem 7.12 of "Uniqueness of smooth cohomology theories" by the authors of this note is not correct. The said theorem identifies the flat part of a differential exte…
Closed manifolds with transcendental L2-Betti numbers
Mikaël Pichot, Thomas Schick, Andrzej Zuk
In this paper, we show how to construct examples of closed manifolds with explicitly computed irrational, even transcendental L2 Betti numbers, defined via the universal covering.…
Hodge Theory on Metric Spaces
Laurent Bartholdi, Thomas Schick, Nat Smale +2
Hodge theory is a beautiful synthesis of geometry, topology, and analysis, which has been developed in the setting of Riemannian manifolds. On the other hand, spaces of images, whi…
A Geometric Description of Equivariant K-Homology for Proper Actions
Paul Baum, Nigel Higson, Thomas Schick
Let G be a discrete group and let X be a G-finite, proper G-CW-complex. We prove that Kasparov's equivariant K-homology groups KK^G(C_0(X),\C) are isomorphic to the geometric equiv…
Differential orbifold K-Theory
Ulrich Bunke, Thomas Schick
We construct differential equivariant K-theory of representable smooth orbifolds as a ring valued functor with the usual properties of a differential extension of a cohomology theo…
Spaces with vanishing $l\sp 2$-homology and their fundamental groups (after Farber and Weinberger)
Nigel Higson, John Roe, Thomas Schick
The "zero in the spectrum conjecture" asserted (in its strongest form) that for any manifold M zero should be in the l2-spectrum of the Laplacian (on forms) of the universal coveri…
Equivariant geometric K-homology for compact Lie group actions
Paul Baum, Herve Oyono-Oyono, Thomas Schick +1
Let G be a compact Lie-group, X a compact G-CW-complex. We define equivariant geometric K-homology groups K^G_*(X), using an obvious equivariant version of the (M,E,f)-picture of B…
Landweber exact formal group laws and smooth cohomology theories
Ulrich Bunke, Thomas Schick, Ingo Schroeder +1
The main aim of this paper is the construction of a smooth (sometimes called differential) extension \hat{MU} of the cohomology theory complex cobordism MU, using cycles for \hat{M…
Smooth K-Theory
Ulrich Bunke, Thomas Schick
We construct an analytic multiplicative model of smooth K-theory. We further introduce the notion of a smooth K-orientation of a proper submersion and define the associated push-fo…