Please use this identifier to cite or link to this item: http://hdl.handle.net/2445/96596
 Title: A Jordan theorem for the diffeomorphism group of some manifolds Author: Mundet i Riera, Ignasi Keywords: Física matemàticaMathematical 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 Related resource: http://dx.doi.org/10.1090/S0002-9939-10-10221-4 URI: http://hdl.handle.net/2445/96596 ISSN: 0002-9939 Appears in Collections: Articles publicats en revistes (Matemàtiques i Informàtica)

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