Addendum to “Coarse homology theories”

In this article, we introduce the notion of a functor on coarse spaces being coarsely excisive-a coarse analogue of the notion of a functor on topological spaces being excisive. Further, taking cones, a coarsely excisive functor yields a topologically excisive functor, and for coarse topological spaces there is an associated coarse assembly map from the topologically exicisive functor to the coarsely excisive functor.We conjecture that this coarse assembly map is an isomorphism for uniformly contractible spaces with bounded geometry, and show that the coarse isomorphism conjecture, along with some mild technical conditions, implies that a correspoding equivariant assembly map is injective. Particular instances of this equivariant assembly map are the maps in the Farrell-Jones conjecture, and in the Baum-Connes conjecture.

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Addendum to “Coarse homology theories”

Abstract: This article corrects two mistakes in the article "Coarse homology theories" [5].

Cited by 3 publications

References 7 publications

The Coarse Baum–connes Conjecture for Relatively Hyperbolic Groups

The Coarse Baum–connes Conjecture for Relatively Hyperbolic Groups

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