no. 4
Bordered Floer homology and incompressible surfaces
[Homologie de Heegaard Floer bordée et surfaces incompressibles]
Alishahi, Akram1 ; Lipshitz, Robert2
1 Department of Mathematics, Columbia University, New York, NY 10027
2 Department of Mathematics, University of Oregon, Eugene, OR 97403
Annales de l'Institut Fourier, Tome 69 (2019) no. 4, pp. 1525-1573.

Nous montrons que l’homologie de Heegaard Floer bordée détecte les disques de compression homologiquement essentiels et que l’homologie de Floer bordée-suturée détecte les enchevêtrements partiellement parallèles au bord, de manière naturelle. Par exemple, il y a un bimodule Λ tel que le produit tensoriel de CFD ^(Y) et Λ est Hom-orthogonal à CFD ^(Y) si et seulement si le bord de Y admet un disque du compression homologiquement essentiel. Nous affinons aussi un résultat de Ni sur la non annulation de l’homologie de Heegaard Floer et nous étendons l’algorithme “factorisation” de Lipshitz–Ozsváth–Thurston  pour calculer l’homologie de Floer bordée-suturée, de sorte que les deux résultats sur la détection des surfaces incompressibles sont effectifs. En particulier, nous montrons que le calcul de l’invariant de l’enchevêtrement de Zarev est combinatoire.

We show that bordered Heegaard Floer homology detects homologically essential compressing disks, and that bordered-sutured Floer homology detects partly boundary-parallel tangles and bridges, in natural ways. For example, there is a bimodule Λ so that the tensor product of CFD ^(Y) and Λ is Hom-orthogonal to CFD ^(Y) if and only if the boundary of Y admits a homologically essential compressing disk. In the process, we sharpen a nonvanishing result of Ni’s. We also extend Lipshitz–Ozsváth–Thurston’s “factoring” algorithm for computing HF ^  to compute bordered-sutured Floer homology, making both results on detecting essential incompressibility practical. In particular, this makes computing Zarev’s tangle invariant manifestly combinatorial.

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Révisé le :
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DOI : 10.5802/aif.3276
Classification : 57M27, 53D40
Keywords: Heegaard Floer homology, bordered Floer homology, sutured manifolds, incompressible surfaces
Mot clés : Homologie de Heegaard Floer, homologie de Floer bordée, variétés suturées, surfaces incompressibles
Alishahi, Akram 1 ; Lipshitz, Robert 2

1 Department of Mathematics, Columbia University, New York, NY 10027
2 Department of Mathematics, University of Oregon, Eugene, OR 97403
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     title = {Bordered {Floer} homology and incompressible surfaces},
     journal = {Annales de l'Institut Fourier},
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     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
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Alishahi, Akram; Lipshitz, Robert. Bordered Floer homology and incompressible surfaces. Annales de l'Institut Fourier, Tome 69 (2019) no. 4, pp. 1525-1573. doi : 10.5802/aif.3276. https://aif.centre-mersenne.org/articles/10.5802/aif.3276/

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