$\ell^p$-coarse Baum-Connes conjecture for $\ell^{q}$-coarse embeddable spaces

TL;DR

This paper establishes an $ ext{ell}^p$-version of the coarse Baum-Connes conjecture for spaces that can be coarsely embedded into $ ext{ell}^q$-spaces, broadening the conjecture's applicability across different $ ext{ell}^p$ and $ ext{ell}^q$ settings.

Contribution

It proves an $ ext{ell}^p$-coarse Baum-Connes conjecture for spaces coarsely embeddable into $ ext{ell}^q$-spaces for all $p, q$ in $[1, olinebreak ext{infty})$, extending previous results.

Findings

Validates the $ ext{ell}^p$-coarse Baum-Connes conjecture for a new class of spaces.

Shows the conjecture holds for spaces coarsely embeddable into any $ ext{ell}^q$-space.

Provides a framework for future research on coarse embeddings and $K$-theoretic conjectures.

Abstract

We prove an $\ell^p$-version of the coarse Baum-Connes conjecture for spaces that coarsely embedds into $\ell^q$-spaces for any $p$ and $q$ in $[1,\infty)$.