Twisted Mazur Pattern Satellite Knots &amp; Bordered Floer Theory

Petkova, Ina; Wong, Biji

doi:10.1307/mmj/20205927

Cited by 2 publications

(1 citation statement)

References 26 publications

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“…In another direction, we extend recent computations of Petkova and Wong in [PW21], where they showed that the genus and fiberedness of the n-twisted Mazur pattern in the solid torus can be determined from the bordered type A structure CFA(S 1 × D 2 , Q 0,1 ), using the bordered pairing theorem and classical results about the genus and fiberedness of satellites knots [Sch53,HMS08]. We expand on these computations and give closed formulas for the genus of n-twisted satellite knots with patterns Q i,j and arbitrary companions, and we determine for which i, j and n the pattern knots Q i,j n are fibered in the solid torus.…”

Section: Introductionmentioning

confidence: 62%

Nontrivial Steenrod squares on prime, hyperbolic and satellite knots

Bodish

2022

Algebr. Geom. Topol.

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We study a family of (1, 1)-pattern knots that generalize the Mazur pattern, and compute the concordance invariants τ and ϵ of n-twisted satellites formed from these patterns. We show that none of the n-twisted patterns from this family act surjectively on the smooth or rational concordance group. We also determine when the n-twisted generalized Mazur patterns are fibered in the solid torus, compute their genus in S 1 × D 2 , and show that n-twisted satellites with generalized Mazur patterns and non-trivial companions are not Floer thin.

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Section: Introductionmentioning

confidence: 62%

Nontrivial Steenrod squares on prime, hyperbolic and satellite knots

Bodish

2022

Algebr. Geom. Topol.

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Heegaard Floer multicurves of double tangles

Zibrowius

2024

Proceedings of Symposia in Pure Mathematics

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We describe a simple formula for computing the Heegaard Floer multicurve invariant of double tangles from the Heegaard Floer multicurve invariant of knot complements. A comparison with a similar multicurve invariant for Conway tangles in the setting of Khovanov homology confirms that knot Floer homology and Khovanov homology behave very differently under satellite operations, echoing recent observations from \cite{LZ}. We also obtain a new characterisation of L-space knots in terms of Heegaard Floer A-link satellites. Along the way, we find the first example of a satellite knot whose knot Floer homology is thin.

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Twisted Mazur Pattern Satellite Knots & Bordered Floer Theory

Cited by 2 publications

References 26 publications

Nontrivial Steenrod squares on prime, hyperbolic and satellite knots

Nontrivial Steenrod squares on prime, hyperbolic and satellite knots

Heegaard Floer multicurves of double tangles

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