Heegaard Floer homology and fibred 3--manifolds

2007/06/14 by Yi Ni, Ni, Yi
Mathematics · #57M27 #57R30 #57R58 #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.GT #msc:57M27 #msc:57R30 #msc:57R58

paper · pdf · doi:10.48550/arxiv.0706.2032

Version 3: 16 pages, 1 figure. This version incorporates the corrigendum to a previous paper. To appear in American Journal of Mathematics. Version 2: Corrects some mistakes in Version 1. The last section of Version 1 is replaced using a quite different and much simpler method. Exposition improved according to the referee's suggestions

openalex publication_date 2007/06/14 · arxiv created 2009/02/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Floer homology and knot complements
• Holomorphic disks and knot invariants
• Holomorphic disks and topological invariants for closed three-manifolds

Related

• On the Heegaard Floer homology of S³_-p/q(K)
• Heegaard diagrams and Floer homology
• Heegaard Floer homology for manifolds with torus boundary: properties and examples
• Heegaard Floer homology of mapping tori II
• Real Heegaard Floer Homology