Volume 24, issue 1 (2020)

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Contact handles, duality, and sutured Floer homology

András Juhász and Ian Zemke

Geometry & Topology 24 (2020) 179–307

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.

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Heegaard Floer homology, cobordism, TQFT
Mathematical Subject Classification 2010
Primary: 57R58
Secondary: 57M27, 57R17
Received: 7 April 2018
Revised: 30 March 2019
Accepted: 20 May 2019
Published: 25 March 2020
Proposed: András I Stipsicz
Seconded: Ciprian Manolescu, Peter Ozsváth
András Juhász
Mathematical Institute
University of Oxford
United Kingdom
Ian Zemke
Department of Mathematics
Princeton University
Princeton, NJ
United States