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

Abstract

In this paper, we verify the ${\ell }^p$ coarse Baum-Connes conjecture for open cones and show that the $K$-theory for ${\ell }^p$ Roe algebras of open cones are independent of $p\in [1,\infty )$. 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.

13 pages, comments are welcome. Small modifications, update references

References in corpus (2)

• K-theory of group Banach algebras and Banach property RD
• Simplicity of reduced group Banach algebras