Hanke, B. and Schick, T.; Enlargeability and index theory: Infinite covers
- Autor: Bernhard Hanke and Thomas Schick
- Titel: "Enlargeability and index theory: Infinite covers"
(dvi) (pdf)
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Preprint, arXiv; to
appear in K-theory
Abstract:
In a previous paper, we showed nonvaninishing of the universal index elements
in
the K-theory of the maximal C*-algebras of the fundamental groups of
enlargeable spin manifolds.
The underlying notion of enlargeability was the one from the first relevant
paper of Gromv and Lawson,
involving contracting maps defined on finite covers of the given manifolds. In
the paper at hand, we weaken this assumption to the one in the second paper of
Gromov and Lawson, where infinite covers are allowed.
The new idea is the construction of a
geometrically given C*-algebra with trace which encodes the information
given by these infinite covers; along the line we obtain an easy proof of a
relative index theorem relevant in this context.
Thomas Schick