K-homological finiteness and hyperbolic groups

Heath Emerson; Bogdan Nica

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arXiv · 1312.4646

K-homological finiteness and hyperbolic groups

Heath Emerson·Bogdan Nica

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Abstract

Motivated by classical facts concerning closed manifolds, we introduce a strong finiteness property in K-homology. We say that a C*-algebra has uniformly summable K-homology if all its K-homology classes can be represented by Fredholm modules which are finitely summable over the same dense subalgebra, and with the same degree of summability. We show that two types of C*-algebras associated to hyperbolic groups - the C*-crossed product for the boundary action, and the reduced group C*-algebra - have uniformly summable K-homology. We provide explicit summability degrees, as well as explicit finitely summable representatives for the K-homology classes.

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BibTeX RIS

Heath Emerson, Bogdan Nica. 2013-12-17. K-homological finiteness and hyperbolic groups. https://arxiv.org/abs/1312.4646

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