Concordance groups of links

Donald, Andrew; Owens, Brendan

doi:10.2140/agt.2012.12.2069

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Concordance groups of links

Andrew Donald and Brendan Owens

Algebraic & Geometric Topology 12 (2012) 2069–2093

DOI: 10.2140/agt.2012.12.2069

Abstract

We define a notion of concordance based on Euler characteristic, and show that it gives rise to a concordance group $ℒ$ of links in $S^{3}$ , which has the concordance group of knots as a direct summand with infinitely generated complement. We consider variants of this using oriented and unoriented surfaces as well as smooth and locally flat embeddings.

Keywords

knots and links, concordance

Mathematical Subject Classification 2010

Primary: 57M25, 57M27, 57N70

References

Publication

Received: 30 April 2012

Revised: 18 July 2012

Accepted: 25 July 2012

Published: 2 December 2012

Authors

Andrew Donald
School of Mathematics and Statistics University of Glasgow 15 University Gardens Glasgow G12 8QW UK

Brendan Owens
School of Mathematics and Statistics University of Glasgow 15 University Gardens Glasgow G12 8QW UK
http://www.maths.gla.ac.uk/~bowens/

Volume 12, issue 4 (2012)