Aula Seminari - Dipartimento di Matematica
Heegaard Floer homology was defined by Ozsváth and Szabó in the early 2000s. It consists of a package of invariants of closed oriented 3-manifolds and it has found many important and profound applications in low dimensional topology. I will introduce the L-space conjecture, that boldly predicts strong connections among properties relating Heegaard Floer homology, foliations and the fundamental group of an irreducible rational homology 3-sphere. I will then state a result concerning this conjecture for manifolds that arise as surgeries on fibered hyperbolic two-bridge links. We will also see how to apply this result to deduce that all non-meridional surgeries on Whitehead doubles of a non-trivial knot support coorientable taut foliations.