Double L–groups and doubly slice knots

Orson, Patrick

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 LL–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 LL–groups in high-dimensional knot theory to define an invariant for doubly slice nn–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 nn–knots for n≥1n≥1.

Citation

Orson, P. (2017). Double L–groups and doubly slice knots. Algebraic & geometric topology, 17(1), 273-329. https://doi.org/10.2140/agt.2017.17.273

• Journal Article Type: Article
• Acceptance Date: May 21, 2016
• Online Publication Date: Jan 26, 2017
• Publication Date: Jan 26, 2017
• Deposit Date: Jun 6, 2016
• Publicly Available Date: Mar 3, 2017
• Journal: Algebraic and Geometric Topology
• Print ISSN: 1472-2747
• Electronic ISSN: 1472-2739
• Publisher: Mathematical Sciences Publishers (MSP)
• Peer Reviewed: Peer Reviewed
• Volume: 17
• Issue: 1
• Pages: 273-329
• DOI: https://doi.org/10.2140/agt.2017.17.273
• Public URL: https://durham-repository.worktribe.com/output/1409970
• Related Public URLs: http://arxiv.org/abs/1508.01048