Topology Seminar: Adam Clay

  • Date: 03/29/2017
  • Time: 15:15
Adam Clay, University of Manitoba

University of British Columbia


The spaces of left and circular orderings of a group


A group is left-orderable if it has a strict total ordering that is invariant under multiplication from the left. For countable groups, this is equivalent to acting on the real line by order-preserving homeomorphisms. A group being circularly orderable has a slightly trickier algebraic definition than left-orderability, but in the countable case boils down, as expected, to the existence of a orientation-preserving action by homeomorphisms on the circle.


The set of all left-orderings of a group forms a topological space, and similarly, so does the set of all circular orderings. I will provide an introduction to these spaces, and discuss recent progress towards understanding the structure of groups whose spaces of circular orderings are “degenerate”, in the sense that they consist simply of a finite set of points with the discrete topology. This is joint work with Cristobal Rivas and Kathryn Mann.

Other Information: 

Location: ESB 4133 (PIMS Lounge)