Finitely summable $\gamma$-elements for word-hyperbolic groups

Abstract

We present two explicit combinatorial constructions of finitely summable reduced “Gamma”-elements ${\gamma }_r\in KK(C_r^{\ast }(\Gamma ),\mathbb{C})$ for any word-hyperbolic group $(\Gamma ,S)$ and obtain summability bounds for them in terms of the cardinality of the generating set $S\subset \Gamma$ and the hyperbolicity constant of the associated Cayley graph.