Topology Seminar: Dale Rolfsen

  • Date: 11/27/2019
  • Time: 14:45
Dale Rolfsen, UBC

University of British Columbia


Ordered groups and n-dimensional dynamics


A group is said to be torsion-free if it has no elements of finite order.  An example is the group, under composition, of self-homeomorphisms (continuous maps with continuous inverses) of the interval I = [0, 1] fixed on the boundary {0, 1}.  In fact this group has the stronger property of being left-orderable, meaning that the elements of the group can be ordered in a way that is invariant under left-multiplication..  If one restricts to piecewise-linear (PL) homeomorphisms, there exists a two-sided (bi-)ordering, an even stronger property of groups.


I will discuss joint work with Danny Calegari concerning groups of homeomorphisms of the cube [0, 1]^n fixed on the boundary.  In the PL category, this group is left-orderable, but not bi-orderable, for all n>1. Also I will report on recent work of James Hyde showing that left-orderability fails for n>1 in the topological category. 

Other Information: 

Location: ESB 4127