Moser's theorem on manifolds with corners

2016/04/30 by Martins Bruveris, Peter W. Michor, Adam Parusinski +1 · 1 citation
Mathematics · #math.DG #msc:53C65 #msc:58A10

paper · pdf · doi:10.1090/proc/14130

published as Proc. Amer. Math. Soc. 146 (2018), No. 11, 4889-4897 · 9 pages; mistakes corrected, final accepted version

arxiv created 2018/02/12 · arxiv updated 2018/10/26

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.

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