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Groups of piecewise linear homeomorphisms of flows

Banff International Research Station for Mathematical Innovation and Discovery

Given a compact space endowed with a flow, every group of orbit-preserving homeomorphisms of the space naturally acts on the real line (identified with an orbit of the flow). This simple observation can be used to define interesting examples of left-orderable groups. In a joint work with Michele Triestino, we explore this idea by defining and studying a class of groups acting on suspension flows of homeomorphisms of the Cantor set. I will explain how this can be used to give a short and conceptual construction of finitely generated simple left-orderable groups, whose existence was recently obtained by Hyde and Lodha. I will also discuss several additional properties of these groups, such as the inability to act on the circle without fixed points, and the lack of subgroups with property (T).

Mathematics; Algebraic topology; Dynamical systems and ergodic theory

video/mp4

Author affiliation: ETH Zurich

2019-12-18

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/72837

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/