K-theory for the maximal Roe algebra of certain expanders
Oyono-Oyono Herv\'e (PIMS), Guoliang Yu
TL;DR
This paper investigates the maximal Roe algebra for certain expanders, establishing its connection to the Baum-Connes conjecture and demonstrating isomorphism results for specific graph families.
Contribution
It introduces a maximal version of the coarse Baum-Connes assembly map and links it to the Baum-Connes map for groups, providing new insights into expanders and K-theory.
Findings
The maximal assembly map is an isomorphism for certain expanders.
The maximal Roe algebra relates closely to the Baum-Connes assembly map.
A new quantitative Baum-Connes assembly map is proposed.
Abstract
We study in this paper the maximal version of the coarse Baum-Connes assembly map for families of expanding graphs arising from residually finite groups. Unlike for the usual Roe algebra, we show that this assembly map is closely related to the (maximal) Baum-Connes assembly map for the group and is an isomorphism for a class of expanders. We also introduce a quantitative Baum-Connes assembly map and discuss its connections to K-theory of (maximal) Roe algebras.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Operator Algebra Research · Homotopy and Cohomology in Algebraic Topology · Geometric and Algebraic Topology