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

Jianguo Zhang

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arXiv · 2111.08860

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

Jianguo Zhang

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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.

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BibTeX RIS

Jianguo Zhang. 2021-11-17. Open Cones and $K$-theory for $\ell^p$ Roe Algebras. https://arxiv.org/abs/2111.08860

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