Graph cobordisms and Heegaard Floer homology

Abstract

We construct a graph TQFT for the minus flavor of Heegaard Floer homology. Our graph TQFT extends Ozsváth and Szabó's TQFT for closed and connected 3-manifolds, and allows for cobordisms with disconnected ends. As an application, we give an explicit formula for the chain homotopy type of the ${\pi }_1$-action on Heegaard Floer homology. We show that on homology the ${\pi }_1$-action is trivial on the plus, minus and infinity flavors, but give examples where it is non-trivial on the hat flavor.

108 pages. Numerous improvements to the presentation. Several aspects of the construction have been streamlined

References in corpus (1)

• On the Colored Jones Polynomial, Sutured Floer homology, and Knot Floer homology

Cited by in corpus (10)

• Link cobordisms and functoriality in link Floer homology
• Connected sums and involutive knot Floer homology
• Duality and mapping tori in Heegaard Floer homology
• An enhanced Euler characteristic of sutured instanton homology
• Geometrically simply connected 4-manifolds and stable cohomotopy Seiberg-Witten invariants
• Projective Naturality in Heegaard Floer Homology
• Involutive Heegaard Floer homology and plumbed three-manifolds
• A connected sum formula for involutive Heegaard Floer homology
• On naturality of the Ozsvath-Szabo contact invariant
• Trisections and Ozsvath-Szabo cobordism invariants