A multivariable Casson–Lin type invariant

Bénard, Léo; Conway, Anthony

doi:10.5802/aif.3330

“…We use Theorem 1.4 to show that the family L t = K 1 t ∪ K 2 t of 2-bridge links from Figure 1 has wsp(L t ) = t. Since the L t are L-space links, their J-functions can be recovered from the potential function [7,Corollary 3.32]. 4 Applying [7,Section 7.4], the potential function of L t is…”

Section: Bounds From Heegaard-floer Homologymentioning

confidence: 99%

“…3 This is the minimal number of crossing changes needed to pass from one given knot to another. 4 Borodzik and Gorsky state this in terms of a symmetrized version ∆ L (t 1 , . .…”

Section: Bounds From Heegaard-floer Homologymentioning

confidence: 99%

A note on the weak splitting number

Cavallo

¹

,

Collari

²

,

Conway

³

2021

Proc. Amer. Math. Soc.

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The weak splitting number wsp(L) of a link L is the minimal number of crossing changes needed to turn L into a split union of knots. We describe conditions under which certain R-valued link invariants give lower bounds on wsp(L). This result is used both to obtain new bounds on wsp(L) in terms of the multivariable signature and to recover known lower bounds in terms of the τ and s-invariants. We also establish new obstructions using link Floer homology and apply all these methods to compute wsp for all but two of the 130 prime links with 9 or fewer crossings.2010 Mathematics Subject Classification. 57M27 (57M25). This work started when the second-named author was visiting the first-named author in Bonn. All three authors are grateful to the Max Plank Institute in Bonn for its support and hospitality. We thank Paolo Lisca and Chuck Livingston for helpful discussions. We are indebted to an anonymous referee for pointing out a mistake in a previous version of this paper, and for their valuable comments.

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“…(2) the slice-torus or signature bound, for the values of ω = 1 used see Table 1; 4 (3) the Alexander polynomial obstructions from [6];…”

Section: The Weak Splitting Number Of Small Linksmentioning

confidence: 99%

A note on the weak splitting number

Cavallo¹,

Collari²,

Conway³

2019

Preprint

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0

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The weak splitting number wsp(L) of a link L is the minimal number of crossing changes needed to turn L into a split union of knots. We describe conditions under which certain R-valued link invariants give lower bounds on wsp(L). This result is used both to obtain new bounds on wsp(L) in terms of the multivariable signature and to recover known lower bounds in terms of the τ and s-invariants. We also establish new obstructions using link Floer homology and apply all these methods to compute wsp for all but two of the 130 prime links with 9 or fewer crossings.2010 Mathematics Subject Classification. 57M27 (57M25). This work started when the second-named author was visiting the first-named author in Bonn. All three authors are grateful to the Max Plank Institute in Bonn for its support and hospitality. We thank Paolo Lisca and Chuck Livingston for helpful discussions.

show abstract