Heegaard Floer homology of broken fibrations over the circle

TL;DR

This paper extends Lagrangian matching invariants to a broader class of 3-manifolds using holomorphic quilts, establishing an isomorphism with Heegaard Floer invariants and providing new calculations and characterizations.

Contribution

It introduces a novel extension of matching invariants to non-fibered 3-manifolds and proves their equivalence with existing Heegaard Floer invariants in specific cases.

Findings

Established isomorphism between extended invariants and Heegaard Floer invariants.

Computed Heegaard Floer homology for new classes of 3-manifolds.

Characterized Juhasz's sutured Floer homology in this context.

Abstract

We extend Perutz's Lagrangian matching invariants to 3-manifolds which are not necessarily fibred using the technology of holomorphic quilts. We prove an isomorphism of these invariants with Ozsvath-Szabo's Heegaard Floer invariants for certain extremal spin^c structures. As applications, we give new calculations of Heegaard Floer homology of certain classes of 3-manifolds, and a characterization of Juhasz's sutured Floer homology.