Floer homology and surface decompositions

2006/09/30 by András Juhász, Andras Juhasz · 5 citations
Mathematics · Medicine · #Alexander polynomial #Botulinum Toxin and Related Neurological Disorders #Combinatorics #Corollary #Fibered knot #Floer homology #Geometric and Algebraic Topology #Homology (biology) #Homotopy and Cohomology in Algebraic Topology #Invariant (physics) #Knot (papermaking) #Knot complement #Knot invariant #Knot theory #Mathematical physics #Mathematics #Pure mathematics #math.GT #msc:57M27 #msc:57R58

paper · pdf · doi:10.2140/gt.2008.12.299

published as Geom. Topol. 12 (2008) 299-350 · 40 pages, 10 figures. Improved, expanded exposition

arxiv created 2007/07/03 · openalex publication_date 2008/03/12 · arxiv updated 2014/11/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Sutured Floer homology, denoted by SFH , is an invariant of balanced sutured manifolds previously defined by the author. In this paper we give a formula that shows how this invariant changes under surface decompositions. In particular, if .M; / .M 0 ; 0 / is a sutured manifold decomposition then SFH .M 0 ; 0 / is a direct summand of SFH .M; /. To prove the decomposition formula we give an algorithm that computes SFH .M; / from a balanced diagram defining .M; / that generalizes the algorithm of Sarkar and Wang.

Citations

• Holomorphic disks and three-manifolds invariants: Properties and applications
• An algorithm for computing some Heegaard Floer homologies
• Holomorphic disks and topological invariants for closed three-manifolds
• Holomorphic disks and genus bounds
• An algorithm for computing some Heegaard Floer homologies

Cited by

• Khovanov homology is an unknot-detector
• Concordance maps in knot Floer homology
• The next-to-top term of the knot Floer homology of some non-fibered knots
• Instanton and the depth of taut foliations
• Floer homology [wikipedia]