The coarse index class with support

Abstract

We construct the coarse index class with support condition (as an element of coarse $K$-homology) of an equivariant Dirac operator on a complete Riemannian manifold endowed with a proper, isometric action of a group. We further show a coarse relative index theorem and discuss the compatibility of the index with the suspension isomorphism.

42 pages: revised version, Section on graded $C^{\ast }$-categories and algebras added

References in corpus (4)

• Equivariant coarse homotopy theory and coarse algebraic $\mathbf{K}$-homology
• Topological equivariant coarse K-homology
• Injectivity results for coarse homology theories
• Localization for coarse homology theories

Cited by in corpus (3)

• Equivariant Callias index theory via coarse geometry
• Localization for coarse homology theories
• Coarse homotopy theory and boundary value problems