A Combinatorial Criterion and Center for the quasi-isometry groups of Euclidean spaces

Abstract

In this study, we introduce the notion of $P{L}_{\delta }$-homeomorphisms of ${\mathbb{R}}^n$. Furthermore, we provide a combinatorial criterion reliant on the vertices and edges of simplicial structures, to determine whether a piecewise-linear homeomorphism to be a quasi-isometry. By employing this criterion, we subsequently show that the center of the group $QI({\mathbb{R}}^n)$, which comprises all quasi-isometries of ${\mathbb{R}}^n$, is indeed trivial.

arXiv comment12 Pages

References in corpus (1)

• On the center of the group of quasi-isometries of the real line