Yash Lodha - Group actions on 1-manifolds by piecewise diffeomorphisms
Channel: Centro de Matemática
Date: 2018-11-13

Yash Lodha (EPFL-Lausanne) 

Group actions on 1-manifolds by piecewise diffeomorphisms

Group actions on 1−manifolds by homeomorphisms that are diffeomorphisms (of desired regularity) outside a countable closed set provide important examples of groups with various exotic features.

Examples of such groups include groups of piecewise linear and piecewise projective homeomorphisms.

It is natural to inquire whether such an action is smoothable, i.e. topologically conjugate to an action by C∞-diffeomorphisms. It is also natural to inquire whether such groups can have property (T). This is a question raised by Navas. I will present recent results (joint works with Matte Bon and Triestino, and with Bonnatti and Triestino) that answer these questions.

I will also briefly discuss the construction of a continuum family (up to isomorphism) of finitely generated simple groups of homeomorphisms of the real line (joint work with James Hyde.) This resolves a 1980 question of Rhemtulla concerning the existence of such groups.

Workshop on Groups, Geometry and Dynamics, 23–27 July 2018, Montevideo, Uruguay.

https://ggdworkshop.cmat.edu.uy/

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