Duality and mapping tori in Heegaard Floer homology

Abstract

We show that the graph TQFT for Heegaard Floer homology satisfies a strong version of Atiyah's duality axiom for a TQFT. As an application, we compute some Heegaard Floer mixed invariants of 4-dimensional mapping tori in terms of Lefschetz numbers on $H{F}^{+}$.

v2: Generalized main theorem slightly to include more cases. New section on perturbed coefficients. Some other small improvements. 77 pages

References in corpus (5)

• Involutive Heegaard Floer homology
• Link cobordisms and functoriality in link Floer homology
• Connected sums and involutive knot Floer homology
• Graph cobordisms and Heegaard Floer homology
• A splitting theorem for the Seiberg-Witten invariant of a homology $S^1\times S^3$

Cited by in corpus (3)

• Contact handles, duality, and sutured Floer homology
• An enhanced Euler characteristic of sutured instanton homology
• Instanton Floer homology, sutures, and Euler characteristics