Open Cones and $K$-theory for $\ell^p$ Roe Algebras

Abstract

In this paper, we verify the ℓ p coarse Baum-Connes conjecture for open cones and show that the K-theory for ℓ p Roe algebras of open cones are independent of p ∈ [1, ∞). Combined with the result of T. Fukaya and S.-I. Oguni, we give 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.