The uniform perfectness of diffeomorphism groups of open manifolds

TL;DR

This paper investigates the algebraic structure of diffeomorphism groups of open and compact manifolds, focusing on properties like uniform perfectness and boundedness, and provides bounds on their diameters related to commutator length.

Contribution

It introduces new bounds on the diameters of diffeomorphism groups with support in balls and conjugation-generated norms, advancing understanding of their algebraic properties.

Findings

Boundedness of diffeomorphism groups established

Upper bounds on diameters with respect to commutator length derived

Results apply to both open and compact manifolds

Abstract

In this paper we study the uniform perfectness, boundedness and uniform simplicity of diffeomorphism groups of compact manifolds with boundary and open manifolds and obtain some upper bounds of their diameters with respect to commutator length, those with support in balls and conjugation-generated norm.