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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
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 (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.

Keywords
string homology, sutures, Floer homology
Mathematical Subject Classification 2010
Primary: 57M50
Secondary: 57R58, 57M27
References
Publication
Received: 9 March 2013
Revised: 13 November 2014
Accepted: 18 November 2014
Published: 22 April 2015
Authors
Daniel V Mathews
School of Mathematical Sciences
Monash University
Building 28, room 401
Clayton VIC 3800
Australia
Eric Schoenfeld
Department of Mathematics
Michigan State University
619 Red Cedar Road
East Lansing, MI 48824
USA