Coarse medians and Property A

TL;DR

This paper proves that certain coarse median spaces with specific properties have Property A, providing an alternative proof that mapping class groups possess this property, which is significant in geometric group theory.

Contribution

It establishes that uniformly locally finite quasigeodesic coarse median spaces of finite rank and controlled growth have Property A, offering a new proof for mapping class groups.

Findings

Coarse median spaces of finite rank have Property A.

Mapping class groups have Property A as a consequence.

Provides an alternative proof for known results about mapping class groups.

Abstract

We prove that uniformly locally finite quasigeodesic coarse median spaces of finite rank and at most exponential growth have Property A. This offers an alternative proof of the fact that mapping class groups have property A.