Abstract

We construct the coarse index class with a support condition of an equivariant Dirac operator on a complete Riemannian manifold endowed with a proper and isometric action of a group as a class of the spectrum-valued equivariant coarse $K$-homology theory ${K\mathcal{𝒳}}^G$ (Ann. K-Theory 8:2 (2023), 141–220). Moreover we show a coarse relative index theorem and discuss the compatibility of the index with the suspension isomorphism.

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