Open Cones and K-Theory for ℓ ^p Roe Algebras

Abstract

In this paper, the author verifies the ℓ ^p coarse Baum-Connes conjecture for open cones and shows that the K-theory for ℓ ^p Roe algebras of open cones is independent of p ∈ [1, ∞). Combined with the result of Fukaya and Oguni, he gives an application to the class of coarsely convex spaces that includes geodesic Gromov hyperbolic spaces, CAT(0)-spaces, certain Artin groups and Helly groups equipped with the word length metric.

Keywords

K-Theory / ℓ ^p Roe algebras / Open cones