Moser’s theorem on manifolds with corners

Bruveris, Martins; Michor, Peter; Parusiński, Adam; Rainer, Armin

doi:10.1090/proc/14130

Moser’s theorem on manifolds with corners
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by Martins Bruveris, Peter W. Michor, Adam Parusiński and Armin Rainer PDF

Proc. Amer. Math. Soc. 146 (2018), 4889-4897 Request permission

Abstract:

Moser’s theorem 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.

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