Dimensionally-reduced sutured Floer homology as a string homology

Abstract

We show that the sutured Floer homology of a sutured 3-manifold of the form $(D^2\times S^1,F\times S^1)$ can be expressed as the homology of a string-type complex, generated by certain sets of curves on $(D^2,F)$ and with a differential given by resolving crossings. We also give some generalisations of this isomorphism, computing "hat" and "infinity" versions of this string homology. In addition to giving interesting elementary facts about the algebra of curves on surfaces, these isomorphisms are inspired by, and establish further, connections between invariants from Floer homology and string topology.

29 pages. v2: a few minor typo corrections and attributions

References in corpus (13)

• HF=HM I : Heegaard Floer homology and Seiberg--Witten Floer homology
• Contact structures, sutured Floer homology and TQFT
• HF=HM III: Holomorphic curves and the differential for the ech/Heegaard Floer correspondence
• The equivalence of Heegaard Floer homology and embedded contact homology via open book decompositions II
• HF=HM IV: The Seiberg-Witten Floer homology and ech correspondence
• Bordered Floer homology for sutured manifolds
• Sutures and contact homology I
• The equivalence of Heegaard Floer homology and embedded contact homology III: from hat to plus
• Embedded contact homology and open book decompositions
• The equivalence of Heegaard Floer homology and embedded contact homology via open book decompositions I
• Itsy bitsy topological field theory
• Sutured Floer homology, sutured TQFT and non-commutative QFT
• The embedded contact homology of sutured solid tori

Cited by in corpus (2)

• On the decategorification of some higher actions in Heegaard Floer homology
• A-infinity algebras, strand algebras, and contact categories