Geodesic
On the equivalence of contact invariants in sutured Floer homology theories
Baldwin, John A1 ; Sivek, Steven2
1 Department of Mathematics, Boston College, Chestnut Hill, MA, United States
2 Department of Mathematics, Imperial College London, London, United Kingdom
Geometry & topology, Tome 25 (2021) no. 3, pp. 1087-1164.

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

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.

DOI : 10.2140/gt.2021.25.1087
Classification : 53D10, 53D40, 57R58
Keywords: contact structures, sutured manifolds, Heegaard Floer homology, monopole Floer homology

Baldwin, John A 1 ; Sivek, Steven 2

1 Department of Mathematics, Boston College, Chestnut Hill, MA, United States
2 Department of Mathematics, Imperial College London, London, United Kingdom 
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Baldwin, John A; Sivek, Steven. On the equivalence of contact invariants in sutured Floer homology theories. Geometry & topology, Tome 25 (2021) no. 3, pp. 1087-1164. doi : 10.2140/gt.2021.25.1087. http://geodesic.mathdoc.fr/articles/10.2140/gt.2021.25.1087/

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