BIRS Workshop Lecture Videos
Groups of piecewise linear homeomorphisms of flows Matte, Nicolás
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).
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