Topology Seminar: Claudius Zibrowius

The Heegaard Floer theory of a 4-ended tangle takes the form of
an immersed curve (with possibly non-trivial local system) on the
boundary of the tangle minus the tangle ends. The Heegaard Floer
homology of a link can be computed as the Lagrangian intersection
theory of the Heegaard Floer homologies of two 4-ended tangles
obtained by splitting the link along an embedded 2-sphere.

 

I will outline the construction of the tangle invariant, with
particular focus on the action of the mapping class group of the
4-punctured sphere. I will then discuss the current state of
symmetry properties for this invariant in the light of the
mutation conjecture.