Diffeomorphism groups of convex polytopes

TL;DR

This paper constructs a regular Lie group structure on the group of all smooth diffeomorphisms of a convex polytope with non-empty interior in a finite-dimensional real vector space.

Contribution

It introduces a novel Lie group structure on the diffeomorphism group of convex polytopes, extending the understanding of geometric transformation groups.

Findings

The diffeomorphism group forms a regular Lie group.

Provides a framework for smooth transformations of convex polytopes.

Enhances the mathematical tools for studying geometric and topological properties of polytopes.

Abstract

Let $E$ be a finite-dimensional real vector space and $M\subseteq E$ be a convex polytope with non-empty interior. We turn the group of all $C^\infty$-diffeomorphisms of $M$ into a regular Lie group.