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Title: | A Jordan theorem for the diffeomorphism group of some manifolds |
Author: | Mundet i Riera, Ignasi |
Keywords: | Física matemàtica Mathematical physics |
Issue Date: | 2010 |
Publisher: | American Mathematical Society (AMS) |
Abstract: | Let $ M$ be a compact connected $ n$-dimensional smooth manifold admitting an unramified covering $ \widetilde{M}\to M$ with cohomology classes $ \alpha_1,\dots,\alpha_n \in H^1(\widetilde{M};\mathbb{Z})$ satisfying $ \alpha_1\cup\dots\cup\alpha_n\neq 0$. We prove that there exists some number $ c$ such that: (1) any finite group of diffeomorphisms of $ M$ contains an abelian subgroup of index at most $ c$; (2) if $ \chi(M)\neq 0$, then any finite group of diffeomorphisms of $ M$ has at most $ c$ elements. We also give a new and short proof of Jordan's classical theorem for finite subgroups of $ \mathrm{GL}(n,\mathbb{C})$, of which our result is an analogue for $ \mathrm{Diff}(M)$. |
Note: | Reproducció del document publicat a: http://dx.doi.org/10.1090/S0002-9939-10-10221-4 |
It is part of: | Proceedings of the American Mathematical Society, 2010, vol. 138, p. 2253-2262 |
URI: | http://hdl.handle.net/2445/96596 |
Related resource: | http://dx.doi.org/10.1090/S0002-9939-10-10221-4 |
ISSN: | 0002-9939 |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
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