A new transfer formalism for coarse K-homology theories yields an operator-free proof of Atiyah's L2-index theorem and a fresh treatment of Higson's counterexample to the coarse Baum-Connes conjecture.
The coarse index class with support
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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.
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Branched coarse coverings and transfer maps
A new transfer formalism for coarse K-homology theories yields an operator-free proof of Atiyah's L2-index theorem and a fresh treatment of Higson's counterexample to the coarse Baum-Connes conjecture.