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Institut de Mathématiques de Marseille, UMR 7373
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A categorified view of the Alexander invariant

09h30 - 10h30
horaire FRUMAM

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.