Heegaard Floer homology solid tori
Liam Watson (University of Glasgow)
Wednesday 23rd October, 2013 16:00-17:00 Maths 204
The Alexander trick shows that any Dehn twist along the meridian of a torus extends to a homeomorphism of the solid torus. In fact, as a consequence of Johannson’s finiteness theorem, this property characterises the solid torus among orientable, irreducible 3-manifolds with torus boundary. We’ll show that this characterisation no longer holds at the level of Heegaard Floer homology. This observation is about bordered Heegaard Floer homology, and in particular, appeals to bimodules in the bordered theory associated with cable spaces. The talk will assume no background from Floer theory and will assume very little from three-manifold topology, focusing instead on the algebraic objects that arise in this theory for three-manifolds with boundary.