2013/12/17 by Heath Emerson, Emerson, Heath, Bogdan Nica +1 · 1 citation
Mathematics · #19K33 #20F67 #58B34 #FOS: Mathematics #Group Theory (math.GR) #K-Theory and Homology (math.KT) #Operator Algebras (math.OA) #math.GR #math.KT #math.OA #msc:19K33 #msc:20F67 #msc:58B34
paper · pdf · doi:10.48550/arxiv.1312.4646
v1: 34 pages, expands and supersedes our preprint `Finitely summable Fredholm modules for boundary actions of hyperbolic groups', arXiv:1208.0856; v2: final version, to appear in Crelle
arxiv created 2015/12/15 · arxiv updated 2015/12/16
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.