scholarly journals Combinatorial Heegaard Floer homology and nice Heegaard diagrams

2012 ◽  
Vol 231 (1) ◽  
pp. 102-171 ◽  
Author(s):  
Peter Ozsváth ◽  
András I. Stipsicz ◽  
Zoltán Szabó
Keyword(s):  
Floer Homology ◽  
Heegaard Floer Homology ◽  
Heegaard Diagrams ◽  
Heegaard Floer

scholarly journals Naturality and Mapping Class Groups in Heegaard Floer Homology

2021 ◽  
Vol 273 (1338) ◽  
Author(s):  
András Juhász ◽  
Dylan Thurston ◽  
Ian Zemke
Keyword(s):  
Fundamental Group ◽  
Floer Homology ◽  
Sufficient Conditions ◽  
Mapping Class Groups ◽  
Heegaard Floer Homology ◽  
Mapping Class ◽  
Class Groups ◽  
Heegaard Diagrams ◽  
Generating Set ◽  
Heegaard Floer

We show that all versions of Heegaard Floer homology, link Floer homology, and sutured Floer homology are natural. That is, they assign concrete groups to each based 3-manifold, based link, and balanced sutured manifold, respectively. Furthermore, we functorially assign isomorphisms to (based) diffeomorphisms, and show that this assignment is isotopy invariant. The proof relies on finding a simple generating set for the fundamental group of the “space of Heegaard diagrams,” and then showing that Heegaard Floer homology has no monodromy around these generators. In fact, this allows us to give sufficient conditions for an arbitrary invariant of multi-pointed Heegaard diagrams to descend to a natural invariant of 3-manifolds, links, or sutured manifolds.

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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