Engel, Alexander (2019) Rough index theory on spaces of polynomial growth and contractibility. JOURNAL OF NONCOMMUTATIVE GEOMETRY, 13 (2). pp. 617-666. ISSN 1661-6952, 1661-6960
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We will show that for a polynomially contractible manifold of bounded geometry and of polynomial volume growth every coarse and rough cohomology class pairs continuously with the K-theory of the uniform Roe algebra. As an application we will discuss non-vanishing of rough index classes of Dirac operators over such manifolds, and we will furthermore get higher-codimensional index obstructions to metrics of positive scalar curvature on closed manifolds with virtually nilpotent fundamental groups. We will give a computation of the homology of (a dense, smooth subalgebra of) the uniform Roe algebra of manifolds of polynomial volume growth.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | CYCLIC COHOMOLOGY; DEHN FUNCTIONS; K-THEORY; CONJECTURE; Novikov conjecture; uniform Roe algebra; uniformly finite homology |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics Mathematics > Prof. Dr. Bernd Ammann |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 21 Apr 2020 08:51 |
| Last Modified: | 21 Apr 2020 08:51 |
| URI: | https://pred.uni-regensburg.de/id/eprint/27791 |
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