Property FW, differentiable structures and smoothability of singular actions

We provide a smoothening criterion for group actions on manifolds by singular diffeomorphisms. We prove that if a countable group Gamma has the fixed point property FW for walls (for example, if it has property(T)), every aperiodic action of Gamma by diffeomorphisms that are of classCrwith countably many singularities is conjugate to an action by true diffeomorphisms of classCron a homeomorphic (possibly non-diffeomorphic) manifold. As applications, we show that Navas's 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.


Published in:
Journal Of Topology, 13, 3, 1119-1138
Year:
Sep 01 2020
Publisher:
Hoboken, WILEY
ISSN:
1753-8416
1753-8424
Keywords:
Laboratories:




 Record created 2020-10-10, last modified 2020-10-27


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