scholarly journals Equivalence of Heegaard Floer homology and embedded contact homology via open book decompositions

2011 ◽  
Vol 108 (20) ◽  
pp. 8100-8105 ◽  
Author(s):  
V. Colin ◽  
P. Ghiggini ◽  
K. Honda
Keyword(s):  
Floer Homology ◽  
Heegaard Floer Homology ◽  
Open Book ◽  
Contact Homology ◽  
Embedded Contact Homology ◽  
Open Book Decompositions ◽  
Heegaard Floer

scholarly journals On the contact Ozsváth-Szabó invariant

2010 ◽  
Vol 47 (1) ◽  
pp. 90-107
Author(s):  
Tolga Etgü ◽  
Burak Ozbagci
Keyword(s):  
Homology Group ◽  
Contact Structure ◽  
Floer Homology ◽  
Heegaard Floer Homology ◽  
Open Book ◽  
Open Book Decomposition ◽  
Heegaard Diagram ◽  
Contact Surgery ◽  
Heegaard Floer

Sarkar and Wang proved that the hat version of Heegaard Floer homology group of a closed oriented 3-manifold is combinatorial starting from an arbitrary nice Heegaard diagram and in fact every closed oriented 3-manifold admits such a Heegaard diagram. Plamenevskaya showed that the contact Ozsváth-Szabó invariant is combinatorial once we are given an open book decomposition compatible with a contact structure. The idea is to combine the algorithm of Sarkar and Wang with the recent description of the contact Ozsváth-Szabó invariant due to Honda, Kazez and Matić. Here we observe that the hat version of the Heegaard Floer homology group and the contact Ozsváth-Szabó invariant in this group can be combinatorially calculated starting from a contact surgery diagram. We give detailed examples pointing out to some shortcuts in the computations.

scholarly journals Heegaard Floer homology as morphism spaces

10.4171/qt/25 ◽  
2011 ◽  
pp. 381-449 ◽  
Author(s):  
Robert Lipshitz ◽  
Peter Ozsváth ◽  
Dylan Thurston
Keyword(s):  
Floer Homology ◽  
Heegaard Floer Homology ◽  
Heegaard Floer

scholarly journals A connected sum formula for involutive Heegaard Floer homology

2017 ◽  
Vol 24 (2) ◽  
pp. 1183-1245 ◽  
Author(s):  
Kristen Hendricks ◽  
Ciprian Manolescu ◽  
Ian Zemke
Keyword(s):  
Floer Homology ◽  
Heegaard Floer Homology ◽  
Connected Sum ◽  
Sum Formula ◽  
Heegaard Floer

Heegaard–Floer homology

Knot Theory ◽  
2018 ◽  
pp. 467-482
Author(s):  
Vassily Manturov
Keyword(s):  
Floer Homology ◽  
Heegaard Floer Homology ◽  
Heegaard Floer

scholarly journals HF=HM, I : Heegaard Floer homology and Seiberg–Witten Floer homology

2020 ◽  
Vol 24 (6) ◽  
pp. 2829-2854
Author(s):  
Çağatay Kutluhan ◽  
Yi-Jen Lee ◽  
Clifford Taubes
Keyword(s):  
Floer Homology ◽  
Heegaard Floer Homology ◽  
Heegaard Floer

scholarly journals Rational cuspidal curves in projective surfaces. Topological versus algebraic obstructions

2017 ◽  
Vol 28 (14) ◽  
pp. 1750106
Author(s):  
Maciej Borodzik
Keyword(s):  
Floer Homology ◽  
Singular Points ◽  
The Other ◽  
Heegaard Floer Homology ◽  
Heegaard Floer ◽  
Bezout Theorem ◽  
Projective Surfaces

We study rational cuspidal curves in projective surfaces. We specify two criteria obstructing possible configurations of singular points that may occur on such curves. One criterion generalizes the result of Fernandez de Bobadilla, Luengo, Melle–Hernandez and Némethi and is based on the Bézout theorem. The other one is a generalization of the result obtained by Livingston and the author and relies on Ozsváth–Szabó inequalities for [Formula: see text]-invariants in Heegaard Floer homology. We show by means of explicit calculations that the two approaches give very similar obstructions.

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