Contact handles, duality, and sutured Floer homology

Abstract

We give an explicit construction of the Honda--Kazez--Matić gluing maps in terms of contact handles. We use this to prove a duality result for turning a sutured manifold cobordism around, and to compute the trace in the sutured Floer TQFT. We also show that the decorated link cobordism maps on the hat version of link Floer homology defined by the first author via sutured manifold cobordisms and by the second author via elementary cobordisms agree.

arXiv comment86 pages, 54 figures, to appear in Geometry and Topology

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Cited by in corpus (8)

• Link cobordisms and functoriality in link Floer homology
• Knot cobordisms, bridge index, and torsion in Floer homology
• Instanton Floer homology, sutures, and Heegaard diagrams
• The cosmetic crossing conjecture for split links
• An enhanced Euler characteristic of sutured instanton homology
• Gluing maps and cobordism maps for sutured monopole Floer homology
• Skein relations for tangle Floer homology
• Trisections and Ozsvath-Szabo cobordism invariants