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 -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.
Cite this article
Alexander Engel, Rough index theory on spaces of polynomial growth and contractibility. J. Noncommut. Geom. 13 (2019), no. 2, pp. 617–666DOI 10.4171/JNCG/335