Mathematics Dept.
  Events
Thomas Hockenhull
University of Glasgow
Wed 20 Nov 2019, 2:45pm
Topology and related seminars
ESB Room 4127 (PIMS)
Koszul duality and Knot Floer homology
ESB Room 4127 (PIMS)
Wed 20 Nov 2019, 2:45pm-3:45pm

Abstract

‘Koszul duality’ is a phenomenon which algebraists are fond of, and has previously been studied in the context of '(bordered) Heegaard Floer homology' by Lipshitz, Ozsváth and Thurston. In this talk, I shall discuss an occurrence of Koszul duality which links older constructions in Heegaard Floer homology with the bordered Heegaard Floer homology of three-manifolds with torus boundary. I shan’t assume any existing knowledge of Koszul duality or any form of Heegaard Floer homology.
hide
UBC
Wed 27 Nov 2019, 2:45pm
Topology and related seminars
ESB 4127 (PIMS)
Ordered groups and n-dimensional dynamics
ESB 4127 (PIMS)
Wed 27 Nov 2019, 2:45pm-3:45pm

Abstract

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.  
hide