The Alexander module, Seifert forms, and categorification

TL;DR

This paper demonstrates that bordered Floer homology categorifies a TQFT, establishing that the Alexander module and Seifert form of a knot are fully determined by Heegaard Floer theory, linking algebraic invariants with topological quantum field theory.

Contribution

It introduces a categorification of Donaldson's TQFT via bordered Floer homology, connecting knot invariants with Floer homology.

Findings

Alexander module determined by Heegaard Floer theory

Seifert form determined by Heegaard Floer theory

Bordered Floer homology categorifies a TQFT

Abstract

We show that bordered Floer homology provides a categorification of a TQFT described by Donaldson. This, in turn, leads to a proof that both the Alexander module of a knot and the Seifert form are completely determined by Heegaard Floer theory.