Contact handles, duality, and sutured Floer homology

Juhász, András; Zemke, Ian

doi:10.2140/gt.2020.24.179

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Contact handles, duality, and sutured Floer homology

András Juhász and Ian Zemke

Geometry & Topology 24 (2020) 179–307

DOI: 10.2140/gt.2020.24.179

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.

Keywords

Heegaard Floer homology, cobordism, TQFT

Mathematical Subject Classification 2010

Primary: 57R58

Secondary: 57M27, 57R17

References

Publication

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

Authors

András Juhász
Mathematical Institute University of Oxford Oxford United Kingdom

Ian Zemke
Department of Mathematics Princeton University Princeton, NJ United States

Volume 24, issue 1 (2020)