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, 2:45pm3:45pm
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 threemanifolds with torus boundary. I shan’t assume any existing knowledge of Koszul duality or any form of Heegaard Floer homology.
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UBC

Wed 27 Nov 2019, 2:45pm
Topology and related seminars
ESB 4127 (PIMS)

Ordered groups and ndimensional dynamics

ESB 4127 (PIMS)
Wed 27 Nov 2019, 2:45pm3:45pm
Abstract
A group is said to be torsionfree if it has no elements of finite order. An example is the group, under composition, of selfhomeomorphisms (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 leftorderable, meaning that the elements of the group can be ordered in a way that is invariant under leftmultiplication.. If one restricts to piecewiselinear (PL) homeomorphisms, there exists a twosided (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 leftorderable, but not biorderable, for all n>1. Also I will report on recent work of James Hyde showing that leftorderability fails for n>1 in the topological category.
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