Embedding certain diffeomorphism groups into the quasi-isometry groups of Euclidean spaces

TL;DR

This paper demonstrates that specific groups of diffeomorphisms and PL-homeomorphisms can be embedded into the quasi-isometry groups of Euclidean spaces, revealing new connections between geometric group theory and topology.

Contribution

It introduces a novel embedding of certain diffeomorphism and PL-homeomorphism groups into the quasi-isometry groups of Euclidean spaces.

Findings

Certain diffeomorphism groups embed into quasi-isometry groups

PL-homeomorphism groups embed into quasi-isometry groups

Establishes new links between topology and geometric group theory

Abstract

We show that certain groups of diffeomorphisms and PL-homeomorphisms embed in the group of all quasi-isometries of the Euclidean spaces.