scholarly journals Grid Diagrams in Heegaard Floer Theory

2013 ◽  
pp. 643-657
Author(s):  
Ciprian Manolescu
Keyword(s):  
Floer Theory ◽  
Grid Diagrams ◽  
Heegaard Floer

scholarly journals On independence of iterated Whitehead doubles in the knot concordance group

2018 ◽  
Vol 27 (01) ◽  
pp. 1850003
Author(s):  
Kyungbae Park
Keyword(s):  
Correction Term ◽  
Khovanov Homology ◽  
Floer Theory ◽  
Knot Concordance ◽  
Torus Knot ◽  
Linearly Independent ◽  
Heegaard Floer

Let [Formula: see text] be the positively clasped untwisted Whitehead double of a knot [Formula: see text], and [Formula: see text] be the [Formula: see text] torus knot. We show that [Formula: see text] and [Formula: see text] are linearly independent in the smooth knot concordance group [Formula: see text] for each [Formula: see text]. Further, [Formula: see text] and [Formula: see text] generate a [Formula: see text] summand in the subgroup of [Formula: see text] generated by topologically slice knots. We use the concordance invariant [Formula: see text] of Manolescu and Owens, using Heegaard Floer correction term. Interestingly, these results are not easily shown using other concordance invariants such as the [Formula: see text]-invariant of knot Floer theory and the [Formula: see text]-invariant of Khovanov homology. We also determine the infinity version of the knot Floer complex of [Formula: see text] for any [Formula: see text] generalizing a result for [Formula: see text] of Hedden, Kim and Livingston.

scholarly journals Combinatorial cobordism maps in hat Heegaard Floer theory

2008 ◽  
Vol 145 (2) ◽  
pp. 207-247 ◽  
Author(s):  
Robert Lipshitz ◽  
Ciprian Manolescu ◽  
Jiajun Wang
Keyword(s):  
Floer Theory ◽  
Heegaard Floer

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
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