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Moser's theorem on manifolds with corners


Authors: Martins Bruveris, Peter W. Michor, Adam Parusiński and Armin Rainer
Journal: Proc. Amer. Math. Soc. 146 (2018), 4889-4897
MSC (2010): Primary 53C65, 58A10
DOI: https://doi.org/10.1090/proc/14130
Published electronically: August 10, 2018
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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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Martins Bruveris
Affiliation: Department of Mathematics, Brunel University London, Uxbridge, UB8 3PH, United Kingdom
Email: martins.bruveris@brunel.ac.uk

Peter W. Michor
Affiliation: Fakultät für Mathematik, Universität Wien, Oskar-Morgenstern-Platz 1, A-1090 Wien, Austria
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
Email: armin.rainer@univie.ac.at

DOI: https://doi.org/10.1090/proc/14130
Keywords: Manifolds with corners, Moser's theorem, Stokes's theorem
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
Article copyright: © Copyright 2018 American Mathematical Society

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