Volume 17, issue 1 (2017)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 24
Issue 6, 2971–3570
Issue 5, 2389–2970
Issue 4, 1809–2387
Issue 3, 1225–1808
Issue 2, 595–1223
Issue 1, 1–594

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN 1472-2739 (online)
ISSN 1472-2747 (print)
Author Index
To Appear
 
Other MSP Journals
Double $L$–groups and doubly slice knots

Patrick Orson

Algebraic & Geometric Topology 17 (2017) 273–329
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.

Keywords
knot theory, L-theory, doubly slice, high-dimensional knot, Blanchfield pairing
Mathematical Subject Classification 2010
Primary: 57Q45
Secondary: 57R67, 57Q60, 57R65
References
Publication
Received: 1 December 2015
Revised: 11 April 2016
Accepted: 21 May 2016
Published: 26 January 2017
Authors
Patrick Orson
Department of Mathematics
Durham University
Lower Mountjoy, Stockton Road
Durham
DH1 3LE
United Kingdom
http://www.maths.dur.ac.uk/~vkdx72/