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.References
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Additional Information
- Martins Bruveris
- Affiliation: Department of Mathematics, Brunel University London, Uxbridge, UB8 3PH, United Kingdom
- MR Author ID: 931234
- Email: martins.bruveris@brunel.ac.uk
- Peter W. Michor
- Affiliation: Fakultät für Mathematik, Universität Wien, Oskar-Morgenstern-Platz 1, A-1090 Wien, Austria
- MR Author ID: 124340
- Email: peter.michor@univie.ac.at
- Adam Parusiński
- Affiliation: Département de Mathématiques, Université Nice Sophia Antipolis, CNRS, LJAD, UMR 7351, 06108 Nice, France
- Email: adam.parusinski@unice.fr
- Armin Rainer
- Affiliation: Fakultät für Mathematik, Universität Wien, Oskar-Morgenstern-Platz 1, A-1090 Wien, Austria
- MR Author ID: 752266
- ORCID: 0000-0003-3825-3313
- Email: armin.rainer@univie.ac.at
- Received by editor(s): January 3, 2017
- Received by editor(s) in revised form: February 12, 2018
- Published electronically: August 10, 2018
- Additional Notes: This work was supported by the Austrian Science Fund (FWF), Grant P 26735-N25, and by a BRIEF Award from Brunel University London.
- Communicated by: Alexander Braverman
- © Copyright 2018 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 146 (2018), 4889-4897
- MSC (2010): Primary 53C65, 58A10
- DOI: https://doi.org/10.1090/proc/14130
- MathSciNet review: 3856155