Coarse dynamics and fixed point property

TL;DR

This paper explores the fixed point property in coarse geometry, establishing a coarse analogue of Brouwer's fixed point theorem by analyzing group actions on coarse spaces and their Higson corona.

Contribution

It introduces a coarse version of Brouwer's fixed point theorem, connecting fixed point properties with coarse geometric structures.

Findings

Established a coarse fixed point theorem analogous to Brouwer's theorem

Analyzed group actions on coarse spaces and Higson corona

Provided new insights into fixed point properties in coarse geometry

Abstract

We investigate the fixed point property of the group actions on a coarse space and its Higson corona. We deduce the coarse version of Brouwer's fixed point theorem.