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Remarks on flat and differential K -theory

Man-Ho Ho (2014)

Annales mathématiques Blaise Pascal

In this note we prove some results in flat and differential K -theory. The first one is a proof of the compatibility of the differential topological index and the flat topological index by a direct computation. The second one is the explicit isomorphisms between Bunke-Schick differential K -theory and Freed-Lott differential K -theory.

Remarks on Yu’s ‘property A’ for discrete metric spaces and groups

Jean-Louis Tu (2001)

Bulletin de la Société Mathématique de France

Guoliang Yu has introduced a property on discrete metric spaces and groups, which is a weak form of amenability and which has important applications to the Novikov conjecture and the coarse Baum–Connes conjecture. The aim of the present paper is to prove that property in particular examples, like spaces with subexponential growth, amalgamated free products of discrete groups having property A and HNN extensions of discrete groups having property A.

The signature package on Witt spaces

Pierre Albin, Éric Leichtnam, Rafe Mazzeo, Paolo Piazza (2012)

Annales scientifiques de l'École Normale Supérieure

In this paper we prove a variety of results about the signature operator on Witt spaces. First, we give a parametrix construction for the signature operator on any compact, oriented, stratified pseudomanifold X which satisfies the Witt condition. This construction, which is inductive over the ‘depth’ of the singularity, is then used to show that the signature operator is essentially self-adjoint and has discrete spectrum of finite multiplicity, so that its index—the analytic signature of  X —is well-defined....

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