Finitely summable γ-elements for word-hyperbolic groups

Jean-Marie Cabrera (1) , Michael Puschnigg (2)

1 AMU - Aix Marseille Université
2 I2M - Institut de Mathématiques de Marseille

We present two explicit combinatorial constructions of finitely summable reduced "Gamma"-elements γ r ∈ KK(C * r (Γ), C) for any word-hyperbolic group (Γ, S) and obtain summability bounds for them in terms of the cardinality of the generating set S ⊂ Γ and the hyperbolicity constant of the associated Cayley graph.

Domaines: K-théorie et homologie [math.KT]

Jean-Marie Cabrera, Michael Puschnigg. Finitely summable γ-elements for word-hyperbolic groups. Journal of Noncommutative Geometry, In press, ⟨10.4171/JNCG/446⟩. ⟨hal-03598326⟩