With Eric Schoenfeld – (42 pages) – on the arXiv – published in Algebraic & Geometric Topology.

Abstract: We show that the sutured Floer homology of a sutured 3-manifold of the form \((D^2 \times S^1, F \times S^1)\) can be expressed as the homology of a string-type complex, generated by certain sets of curves on \((D^2, F)\) 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.

Dimensionally_reduced_SFH_string_homology_AGT
Dimensionally-reduced sutured Floer homology as a string homology

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