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On the equivalence of contact invariants in sutured Floer homology theories

John A Baldwin and Steven Sivek

Geometry & Topology 25 (2021) 1087–1164

We recently defined an invariant of contact manifolds with convex boundary in Kronheimer and Mrowka’s sutured monopole Floer homology theory. Here, we prove that there is an isomorphism between sutured monopole Floer homology and sutured Heegaard Floer homology which identifies our invariant with the contact class defined by Honda, Kazez and Matić in the latter theory. One consequence is that the Legendrian invariants in knot Floer homology behave functorially with respect to Lagrangian concordance. In particular, these invariants provide computable and effective obstructions to the existence of such concordances. Our work also provides the first proof which does not rely on Giroux’s correspondence that Honda, Kazez and Matić’s contact class is well defined up to isomorphism.

contact structures, sutured manifolds, Heegaard Floer homology, monopole Floer homology
Mathematical Subject Classification 2010
Primary: 53D10
Secondary: 53D40, 57R58
Received: 19 January 2016
Revised: 18 May 2020
Accepted: 8 July 2020
Published: 20 May 2021
Proposed: Yasha Eliashberg
Seconded: András I Stipsicz, Paul Seidel
John A Baldwin
Department of Mathematics
Boston College
Chestnut Hill, MA
United States
Steven Sivek
Department of Mathematics
Imperial College London
United Kingdom