A Lie group structure on the group of real analytic diffeomorphisms of a compact real analytic manifold with corners

TL;DR

This paper establishes a smooth Lie group structure on the group of real analytic diffeomorphisms of compact manifolds with corners, extending previous results to more complex geometries with a novel construction method.

Contribution

It introduces a new approach to define a Lie group structure on diffeomorphisms of manifolds with corners, generalizing prior work on manifolds without corners.

Findings

Lie group structure successfully constructed

Method applicable to manifolds with corners

Extends known results to more general manifolds

Abstract

We construct a smooth Lie group structure on the group of real analytic diffeomorphisms of a compact analytic manifold with corners. This generalises the known analogous results in the situation where the real analytic manifold has no corners. Additionally our approach uses a different construction.