Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 15, Number 2 (2015), 691-731.
Dimensionally reduced sutured Floer homology as a string homology
We show that the sutured Floer homology of a sutured –manifold of the form can be expressed as the homology of a string-type complex, generated by certain sets of curves on 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.
Algebr. Geom. Topol., Volume 15, Number 2 (2015), 691-731.
Received: 9 March 2013
Revised: 13 November 2014
Accepted: 18 November 2014
First available in Project Euclid: 28 November 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 57M50: Geometric structures on low-dimensional manifolds
Secondary: 57R58: Floer homology 57M27: Invariants of knots and 3-manifolds
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