Divergence functions of higher-dimensional Thompson's groups

TL;DR

This paper proves that higher-dimensional Thompson's groups exhibit linear divergence functions, which implies their asymptotic cones do not have cut-points, advancing understanding of their geometric properties.

Contribution

It establishes the linear divergence of higher-dimensional Thompson's groups, a novel result linking group divergence to asymptotic cone topology.

Findings

Higher-dimensional Thompson's groups have linear divergence functions

Their asymptotic cones do not contain cut-points

Advances understanding of geometric group properties

Abstract

We prove that higher-dimensional Thompson's groups have linear divergence functions. By the work of Dru\c{t}u, Mozes, and Sapir, this implies none of the asymptotic cones of $nV$ has a cut-point.