$L^p$ Coarse Baum-Connes Conjecture and $K$-theory for $L^p$ Roe Algebras

TL;DR

This paper proves the $L^p$ coarse Baum-Connes conjecture for spaces with finite asymptotic dimension across a range of p values and shows the $K$-theory of $L^p$ Roe algebras is p-independent for such spaces.

Contribution

It verifies the $L^p$ coarse Baum-Connes conjecture for finite asymptotic dimension spaces and demonstrates $K$-theory independence from p in this setting.

Findings

Verification of the $L^p$ coarse Baum-Connes conjecture for spaces with finite asymptotic dimension.

Demonstration that $K$-theory of $L^p$ Roe algebras is independent of p for these spaces.

Extension of known results to a broader class of spaces and p-values.

Abstract

In this paper, we verify the $L^p$ coarse Baum-Connes conjecture for spaces with finite asymptotic dimension for $p\in[1,\infty)$. We also show that the $K$-theory of $L^p$ Roe algebras are independent of $p\in(1,\infty)$ for spaces with finite asymptotic dimension.