Property FW, differentiable structures, and smoothability of singular actions

Abstract : We provide a smoothening criterion for group actions on manifolds by singular diffeomorphisms. We prove that if a countable group Γ has the fixed point property FW for walls (e.g. if it has property (T)), every aperiodic action of Γ by diffeomorphisms that are of class C r with countably many singularities is conjugate to an action by diffeomorphisms of class C r on a homeomorphic (possibly non-diffeomorphic) manifold. As applications, we show that Navas's rigidity result for actions of Kazhdan groups on the circle, as well as the recent solutions to Zimmer's conjecture, generalise to aperiodic actions by diffeomorphisms with countably many singularities. 1
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Contributeur : Michele Triestino <>
Soumis le : lundi 26 mars 2018 - 20:39:12
Dernière modification le : vendredi 8 juin 2018 - 14:50:07

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  • HAL Id : hal-01743993, version 1
  • ARXIV : 1803.08567

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Yash Lodha, Nicolás Matte Bon, Michele Triestino. Property FW, differentiable structures, and smoothability of singular actions. 19 pages. 2018. 〈hal-01743993〉

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