## Algebraic & Geometric Topology

### 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 $(D2 × S1,F × S1)$ can be expressed as the homology of a string-type complex, generated by certain sets of curves on $(D2,F)$ 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.

#### Article information

Source
Algebr. Geom. Topol., Volume 15, Number 2 (2015), 691-731.

Dates
Revised: 13 November 2014
Accepted: 18 November 2014
First available in Project Euclid: 28 November 2017

https://projecteuclid.org/euclid.agt/1511895786

Digital Object Identifier
doi:10.2140/agt.2015.15.691

Mathematical Reviews number (MathSciNet)
MR3342673

Zentralblatt MATH identifier
1330.57026

#### Citation

Mathews, Daniel V; Schoenfeld, Eric. Dimensionally reduced sutured Floer homology as a string homology. Algebr. Geom. Topol. 15 (2015), no. 2, 691--731. doi:10.2140/agt.2015.15.691. https://projecteuclid.org/euclid.agt/1511895786

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