Rough index theory on spaces of polynomial growth and contractibility

2015/05/15 by Engel, Alexander · 1 citation
#19K56 (Secondary) #46L80 #58J22 (Primary) #Differential Geometry (math.DG) #FOS: Mathematics #K-Theory and Homology (math.KT)

paper · doi:10.48550/arxiv.1505.03988

Abstract

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.

Cited by

• Asymptotic expansion for groupoids and Roe type algebras

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