#### Volume 15, issue 2 (2015)

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Dimensionally reduced sutured Floer homology as a string homology

### Daniel V Mathews and Eric Schoenfeld

Algebraic & Geometric Topology 15 (2015) 691–731
##### Abstract

We show that the sutured Floer homology of a sutured $3$–manifold of the form $\left({D}^{2}×{S}^{1},F×{S}^{1}\right)$ can be expressed as the homology of a string-type complex, generated by certain sets of curves on $\left({D}^{2},F\right)$ 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.

##### Keywords
string homology, sutures, Floer homology
##### Mathematical Subject Classification 2010
Primary: 57M50
Secondary: 57R58, 57M27