Conjugation-invariant norms on groups of geometric origin

TL;DR

This paper investigates the boundedness of groups of diffeomorphisms by examining their properties under bi-invariant metrics, contributing to understanding their geometric structure.

Contribution

It introduces new results on the boundedness of diffeomorphism groups, expanding the knowledge of their geometric and algebraic properties.

Findings

Certain diffeomorphism groups are bounded under bi-invariant metrics

Boundedness depends on the group's geometric structure

Results provide insights into the metric properties of geometric groups

Abstract

A group is said to be bounded if it has a finite diameter with respect to any bi-invariant metric. In the present paper we discuss boundedness of various groups of diffeomorphisms.