Geometry and Topology Seminar: "Heegaard Floer homology and branched double covers"

Abstract: The L-space conjecture is a curious conjecture which relates various aspects of three-manifolds: orderability of the fundamental group, Floer homology, and the existence of taut foliations. Using simple properties of the fundamental group, this conjecture predicts several natural properties for Floer homology and foliations, including their behavior under maps between three-manifolds. We will then use some techniques from symplectic geometry to prove one of these predictions for how Heegaard Floer homology behaves under branched double covers. This is preliminary work in progress with Kristen Hendricks and Robert Lipshitz.

Host: Aliakbar Daemi