Moser's theorem on manifolds with corners

TL;DR

This paper extends Moser's theorem to manifolds with corners, including simplices, using a cohomological approach and building on Banyaga's work for manifolds with boundary.

Contribution

It generalizes Moser's theorem to manifolds with corners and provides a cohomological interpretation of Banyaga's operator.

Findings

Moser's theorem holds for manifolds with corners.

A cohomological interpretation of Banyaga's operator is established.

Lefschetz duality is proved using differential forms.

Abstract

Moser's theorem (1965) states that the diffeomorphism group of a compact manifold acts transitively on the space of all smooth positive densities with fixed volume. Here we describe the extension of this result to manifolds with corners. In particular we obtain Moser's theorem on simplices. The proof is based on Banyaga's paper (1974), where Moser's theorem is proven for manifolds with boundary. A cohomological interpretation of Banyaga's operator is given, which allows a proof of Lefschetz duality using differential forms.