The Alexander module, Seifert forms, and categorification

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.

80 pages, 21 figures, uses color Version 2: Minor edits as suggested by the referee. This version accepted for publication by the Journal of Topology

References in corpus (5)

• Floer homology and knot complements
• On the Khovanov and knot Floer homologies of quasi-alternating links
• Bordered Floer homology for sutured manifolds
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Cited by in corpus (5)

• A calculus for bordered Floer homology
• Bordered Floer homology and incompressible surfaces
• A bordered HF- algebra for the torus
• On the decategorification of some higher actions in Heegaard Floer homology
• A Floer homology invariant for $3$-orbifolds via bordered Floer theory