Heegaard Floer homology and fibred 3--manifolds

TL;DR

This paper demonstrates that Heegaard Floer homology can determine if a closed 3-manifold fibers over the circle with a fiber of negative Euler characteristic, extending previous knot results.

Contribution

It establishes a new criterion using Heegaard Floer homology to identify fibred 3-manifolds, generalizing earlier knot-based findings.

Findings

Heegaard Floer homology detects fibred structures in 3-manifolds

Extension of knot fibering results to closed 3-manifolds

Provides a new tool for classifying fibred 3-manifolds

Abstract

Given a closed 3--manifold $Y$, we show that the Heegaard Floer homology determines whether $Y$ fibres over the circle with a fibre of negative Euler characteristic. This is an analogue of an earlier result about knots proved by Ghiggini and the author.