Dimensionally reduced sutured Floer homology as a string homology

Daniel Mathews, Eric Schoenfeld

Research output: Contribution to journalArticleResearchpeer-review

Abstract

We show that the sutured Floer homology of a sutured 33–manifold of the form (D2×S1,F×S1)(D2×S1,F×S1) can be expressed as the homology of a string-type complex, generated by certain sets of curves on (D2,F)(D2,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.
Original languageEnglish
Pages (from-to)691-731
Number of pages41
JournalAlgebraic and Geometric Topology
Volume15
Issue number2
DOIs
Publication statusPublished - 2015

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