On certain elements and the center of the quasi-isometry groups of Euclidean spaces

Swarup Bhowmik, Prateep Chakraborty

Published 2022-02-08Version 1

We introduce the notion of $PL_\delta$- homeomorphism between two locally finite simplicial complexes in $\mathbb{R}^n$ and give a sufficient condition for a simplicial homeomorphism to be a quasi-isometry. We show that the center of the group $QI(\mathbb{R}^n)$ of all quasi-isometries of $\mathbb{R}^n$ is trivial.