A categorified view of the Alexander invariant
Aix-Marseille Université - Site St Charles
3, place Victor Hugo - case 39
13331 MARSEILLE Cedex 03
Alexander invariants are classical objects in low-dimensional topology stemming from a natural module structure on the homology of the universal abelian cover. This is the natural setting in which to define the Alexander polynomial of a knot, for example, and given that this polynomial arises as graded Euler characteristic in knot Floer homology, it is natural to ask if there is a Floer-theoretic counterpart to the Alexander invariant. There is : This talk will describe a TQFT due to Donaldson, explain how it is categorified by bordered Heegaard Floer homology, and from this place the Alexander invariant in a Heegaard Floer setting. This is joint work with Jen Hom and The Lidman.