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On
the equivalence of contact invariants in sutured Floer
homology theories
John A Baldwin and Steven Sivek |
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Geometry & Topology 25 (2021) 1087–1164
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Abstract |
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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. |
Keywords
contact structures, sutured manifolds, Heegaard Floer
homology, monopole Floer homology
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Mathematical Subject Classification 2010
Primary: 53D10
Secondary: 53D40, 57R58
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References |
Publication
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
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Authors |
| John A Baldwin | |
| Department of Mathematics Boston College Chestnut Hill, MA United States |
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| https://sites.google.com/bc.edu/john-baldwin/ | |
| Steven Sivek | |
| Department of Mathematics Imperial College London London United Kingdom |
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| http://wwwf.imperial.ac.uk/~ssivek/ | |
