CAT(0) spaces with polynomial divergence of geodesics

TL;DR

This paper constructs specific CAT(0) spaces with polynomial divergence of geodesics, answering an open question about their existence and expanding understanding of geometric group theory.

Contribution

It provides explicit examples of CAT(0) complexes with polynomial divergence, demonstrating their existence for any desired degree.

Findings

Existence of CAT(0) complexes with polynomial divergence of any degree

Construction method for finite 2-complexes with prescribed divergence

Resolution of Gersten's open question

Abstract

We construct a family of finite 2-complexes whose universal covers are CAT(0) and have polynomial divergence of desired degree. This answers a question of Gersten, namely whether such CAT(0) complexes exist.