On equivariant slice knots

Choon, Jae; Ko, Ki Hyoung

doi:10.1090/s0002-9939-99-04868-6

Cited by 16 publications

(84 citation statements)

References 8 publications

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“…This obstruction takes the form of the non-existence of a certain equivariant lattice embedding which can be checked combinatorially. Identifying the intersection form of the double branched cover of 𝐵 4 over a spanning surface with the Gordon-Litherland form, we prove the following theorem. Theorem 1.1.…”

Section: F I G U R Ementioning

confidence: 99%

Equivariant 4‐genera of strongly invertible and periodic knots

Boyle

Issa

2022

Journal of Topology

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Section: F I G U R Ementioning

confidence: 99%

Equivariant 4‐genera of strongly invertible and periodic knots

Boyle

Issa

2022

Journal of Topology

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“…By using the criteria, she presented examples of slice periodic knots which are not equivariantly slice. (See Davis-Naik [17] and Cha-Ko [12] for further development. )…”

Section: Equivariant 4-genusmentioning

confidence: 99%

Invariant Seifert surfaces for strongly invertible knots

Hirasawa¹,

Hiura²,

Sakuma³

2022

Preprint

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We study invariant Seifert surfaces for strongly invertible knots, and prove that the gap between the equivariant genus (the minimum of the genera of invariant Seifert surfaces) of a strongly invertible knot and the (usual) genus of the underlying knot can be arbitrary large. This forms a sharp contrast with Edmonds' theorem that every periodic knot admits an invariant minimal genus Seifert surface. We also prove variants of Edmonds' theorem, which are useful in studying invariant Seifert surfaces for strongly invertible knots.

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“…There are many linking number one 2-component links which are not concordant, as can be detected, for example, by the multivariable Alexander polynomial [Kaw78,Nak78]. For related in-depth study, the reader is referred to, for instance, [CK99,FP,Cha]. With our respective coauthors, we gave non-concordant linking number one links with two unknotted components, for which abelian invariants such as the multivariable Alexander polynomial are unable to obstruct them from being concordant.…”

Section: Link Concordance Versus Zero Surgery Homology Cobordismmentioning

confidence: 99%

Nonconcordant links with homology cobordant zero-framed surgery manifolds

Choon

Powell

2014

Pacific J. Math.

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The full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. NONCONCORDANT LINKS WITH HOMOLOGY COBORDANT ZERO-FRAMED SURGERY MANIFOLDS JAE CHOON CHA AND MARK POWELLWe use topological surgery theory to give sufficient conditions for the zeroframed surgery manifold of a 3-component link to be homology cobordant to the zero-framed surgery on the Borromean rings (also known as the 3-torus) via a topological homology cobordism preserving the free homotopy classes of the meridians. This enables us to give examples of 3-component links with unknotted components and vanishing pairwise linking numbers, such that any two of these links have homology cobordant zero-surgeries in the above sense, but the zero-surgery manifolds are not homeomorphic. Moreover, the links are not concordant to one another, and in fact they can be chosen to be height h but not height h + 1 symmetric grope concordant, for each h which is at least three.

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On equivariant slice knots

Cited by 16 publications

References 8 publications

Equivariant 4‐genera of strongly invertible and periodic knots

Equivariant 4‐genera of strongly invertible and periodic knots

Invariant Seifert surfaces for strongly invertible knots

Nonconcordant links with homology cobordant zero-framed surgery manifolds

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