Taut foliations on graph manifolds
Liam Watson (University of Glasgow)
Wednesday 20th January, 2016 16:00-17:00 Maths 522
An L-space is a rational homology sphere with simplest possible Heegaard Floer homology. Ozsváth and Szabó have shown that if a closed, connected, orientable three-manifold has a C^2 coorientable taut foliation then it is not an L-space, and it has been recently shown that the C^2 condition can be replaced by C^0 in work of Bowden/Kazez and Roberts. The converse to this statement holds when restricting to graph manifolds; this is part of a joint project with J. Hanselman, J. Rasmussen, and S. Rasmussen. The goal of this talk will be to first introduce the various moving parts in the previous statement (Heegaard Floer homology, foliations, left-orderable groups, etc.) and second to explain the gluing theorem that plugs into this by introducing a calculus for studying bordered Floer homology developed in joint work with J. Hanselman (the underpinnings of which are decidedly algebraic).