scholarly journals Knot concordance and Heegaard Floer homology invariants in branched covers

2008 ◽  
Vol 12 (4) ◽  
pp. 2249-2275 ◽  
Author(s):  
J Elisenda Grigsby ◽  
Daniel Ruberman ◽  
Sašo Strle
Keyword(s):  
Floer Homology ◽  
Heegaard Floer Homology ◽  
Branched Covers ◽  
Knot Concordance ◽  
Heegaard Floer

scholarly journals Tau invariants for balanced spatial graphs

2020 ◽  
Vol 29 (09) ◽  
pp. 2050066
Author(s):  
Katherine Vance
Keyword(s):  
Lower Bound ◽  
Floer Homology ◽  
Chain Complex ◽  
Homology Theory ◽  
Heegaard Floer Homology ◽  
Combinatorial Proof ◽  
Knot Concordance ◽  
Spatial Graphs ◽  
Heegaard Floer ◽  
Definition Of

In 2003, Ozsváth and Szabó defined the concordance invariant [Formula: see text] for knots in oriented 3-manifolds as part of the Heegaard Floer homology package. In 2011, Sarkar gave a combinatorial definition of [Formula: see text] for knots in [Formula: see text] and a combinatorial proof that [Formula: see text] gives a lower bound for the slice genus of a knot. Recently, Harvey and O’Donnol defined a relatively bigraded combinatorial Heegaard Floer homology theory for transverse spatial graphs in [Formula: see text], extending HFK for knots. We define a [Formula: see text]-filtered chain complex for balanced spatial graphs whose associated graded chain complex has homology determined by Harvey and O’Donnol’s graph Floer homology. We use this to show that there is a well-defined [Formula: see text] invariant for balanced spatial graphs generalizing the [Formula: see text] knot concordance invariant. In particular, this defines a [Formula: see text] invariant for links in [Formula: see text]. Using techniques similar to those of Sarkar, we show that our [Formula: see text] invariant is an obstruction to a link being slice.

scholarly journals Primary decomposition in the smooth concordance group of topologically slice knots

2021 ◽  
Vol 9 ◽  
Author(s):  
Jae Choon Cha
Keyword(s):  
Floer Homology ◽  
Heegaard Floer Homology ◽  
Primary Decomposition ◽  
Direct Sum ◽  
Infinite Rank ◽  
Knot Concordance ◽  
Large Subgroup ◽  
Heegaard Floer

Abstract We address primary decomposition conjectures for knot concordance groups, which predict direct sum decompositions into primary parts. We show that the smooth concordance group of topologically slice knots has a large subgroup for which the conjectures are true and there are infinitely many primary parts, each of which has infinite rank. This supports the conjectures for topologically slice knots. We also prove analogues for the associated graded groups of the bipolar filtration of topologically slice knots. Among ingredients of the proof, we use amenable $L^2$ -signatures, Ozsváth-Szabó d-invariants and Némethi’s result on Heegaard Floer homology of Seifert 3-manifolds. In an appendix, we present a general formulation of the notion of primary decomposition.

scholarly journals A survey on Heegaard Floer homology and concordance

2017 ◽  
Vol 26 (02) ◽  
pp. 1740015 ◽  
Author(s):  
Jennifer Hom
Keyword(s):  
Floer Homology ◽  
Heegaard Floer Homology ◽  
Survey Paper ◽  
Stable Equivalence ◽  
Knot Concordance ◽  
Heegaard Floer ◽  
The Way

In this survey paper, we discuss several different knot concordance invariants coming from the Heegaard Floer homology package of Ozsváth and Szabó. Along the way, we prove that if two knots are concordant, then their knot Floer complexes satisfy a certain type of stable equivalence.

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
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