Cobordism of Knots and Blanchfield Duality

Kearton, C.

doi:10.1112/jlms/s2-10.4.406

Cited by 39 publications

(32 citation statements)

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“…The following corollary was already shown to be true by Kearton [5,Corollary 3], but Proposition 4.11 combined with Proposition 3.24 gives a different proof.…”

Section: Definition 410mentioning

confidence: 94%

Double L–groups and doubly slice knots

Orson

2017

Algebr. Geom. Topol.

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Use policyThe 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. Double L-groups and doubly slice knots PATRICK ORSONWe develop a theory of chain complex double cobordism for chain complexes equipped with Poincaré duality. The resulting double cobordism groups are a refinement of the classical torsion algebraic L-groups for localisations of a ring with involution. The refinement is analogous to the difference between metabolic and hyperbolic linking forms.We apply the double L-groups in high-dimensional knot theory to define an invariant for doubly slice n-knots. We prove that the "stably doubly slice implies doubly slice" property holds (algebraically) for Blanchfield forms, Seifert forms and for the Blanchfield complexes of n-knots for n 1.57Q45; 57R67, 57Q60, 57R65

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“…The following corollary was already shown to be true by Kearton [5,Corollary 3], but Proposition 4.11 combined with Proposition 3.24 gives a different proof.…”

Section: Definition 410mentioning

confidence: 94%

Double L–groups and doubly slice knots

Orson

2017

Algebr. Geom. Topol.

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“…There is a correspondence between this and Levine's approach, first proven by Cherry Kearton [15]. (Another source is the appendix A of Litherland's note [23], but beware of diverse typos in the published version.)…”

Section: Linking Pairings and Metabolizersmentioning

confidence: 99%

Some examples related to knot sliceness

Stoimenow

2007

Journal of Pure and Applied Algebra

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“…For proofs of its equivalence to the standard definition in terms of Seifert forms, see Kearton [13] and Ranicki [23]. …”

Section: Extracting First Order Obstructionsmentioning

confidence: 99%

A second order algebraic knot concordance group

Powell

2012

Algebr. Geom. Topol.

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We define an algebraic group comprising symmetric chain complexes which captures the first two stages of the Cochran-Orr-Teichner solvable filtration of the knot concordance group in a single invariant. To achieve this we impose additional structure on each chain complex which puts extra control on the fundamental groups, and in particular on the way in which they can change in a concordance.Comment: 51 pages, 2 figures. This a considerably shortened version of arXiv:1109.0761, to appear in Algebraic and Geometric Topolog

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Cobordism of Knots and Blanchfield Duality

Cited by 39 publications

References 1 publication

Double L–groups and doubly slice knots

Double L–groups and doubly slice knots

Some examples related to knot sliceness

A second order algebraic knot concordance group

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