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2017 Double $L$–groups and doubly slice knots
Patrick Orson
Algebr. Geom. Topol. 17(1): 273-329 (2017). DOI: 10.2140/agt.2017.17.273

Abstract

We 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.

Citation

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Patrick Orson. "Double $L$–groups and doubly slice knots." Algebr. Geom. Topol. 17 (1) 273 - 329, 2017. https://doi.org/10.2140/agt.2017.17.273

Information

Received: 1 December 2015; Revised: 11 April 2016; Accepted: 21 May 2016; Published: 2017
First available in Project Euclid: 16 November 2017

zbMATH: 1358.57027
MathSciNet: MR3604378
Digital Object Identifier: 10.2140/agt.2017.17.273

Subjects:
Primary: 57Q45
Secondary: 57Q60, 57R65, 57R67

Rights: Copyright © 2017 Mathematical Sciences Publishers

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Vol.17 • No. 1 • 2017
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