Twisted Mazur Pattern Satellite Knots & Bordered Floer Theory

2021 ◽  
Vol -1 (-1) ◽  
Author(s):  
Ina Petkova ◽  
Biji Wong
Keyword(s):  
Floer Theory ◽  
Satellite Knots

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 On the Upsilon invariant and satellite knots

2018 ◽  
Vol 292 (3-4) ◽  
pp. 1431-1452
Author(s):  
Peter Feller ◽  
JungHwan Park ◽  
Arunima Ray
Keyword(s):  
Satellite Knots

scholarly journals Covariantly functorial wrapped Floer theory on Liouville sectors

2019 ◽  
Vol 131 (1) ◽  
pp. 73-200 ◽  
Author(s):  
Sheel Ganatra ◽  
John Pardon ◽  
Vivek Shende
Keyword(s):  
Floer Theory

The Neuwirth Conjecture for a family of satellite knots

2019 ◽  
Vol 28 (02) ◽  
pp. 1950017
Author(s):  
Mario Eudave-Muñoz ◽  
José Frías
Keyword(s):  
Closed Surface ◽  
Explicit Constructions ◽  
Satellite Knots

Let [Formula: see text] be a nontrivial knot in [Formula: see text]. It was conjectured that there exists a Neuwirth surface for [Formula: see text]. That is, a closed surface in [Formula: see text] containing the knot [Formula: see text] as a nonseparating curve and such that every compressing disk for the surface intersects the knot in at least two points. We provide explicit constructions of Neuwirth surfaces for a family of satellite knots, which do not depend on the existence of nonorientable algebraically incompressible and [Formula: see text]-incompressible spanning surfaces for these knots.

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