Dimensionally reduced sutured Floer homology as a string homology

Mathews, Daniel V¹ ; Schoenfeld, Eric²

¹School of Mathematical Sciences, Monash University, Building 28, room 401, Clayton VIC 3800, Australia
²Department of Mathematics, Michigan State University, 619 Red Cedar Road, East Lansing, MI 48824, USA

Algebraic and Geometric Topology, Tome 15 (2015) no. 2, pp. 691-731

Résumé

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.

Détail

DOI : 10.2140/agt.2015.15.691

Classification : 57M50, 57R58, 57M27
Keywords: string homology, sutures, Floer homology

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