Volume 14, issue 3 (2014)

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

Volume 17
Issue 6, 3213–3852
Issue 5, 2565–3212
Issue 4, 1917–2564
Issue 3, 1283–1916
Issue 2, 645–1281
Issue 1, 1–643

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
Subscriptions
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Author Index
To Appear
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Infection by string links and new structure in the knot concordance group

John R Burke

Algebraic & Geometric Topology 14 (2014) 1577–1626
Abstract

This paper highlights the importance of string link concordance in the understanding of knot concordance in general. The results of this paper show that there are infinitely many nontrivial knots in the groups Gn of n–solvable knots modulo n.5–solvable knots, for n greater than or equal to 2, which are not concordant to any knot that is obtained by two or more iterated infections of an Arf invariant zero knot by knots. This latter class accounts for nearly all previously known examples of knots in Gn, n greater than or equal to 2.

In this paper we will generalize the concept of when a rational Laurent polynomial is strongly coprime to another, first introduced by Cochran, Harvey and Leidy, to include multivariable polynomials. We also prove the existence of multivariable polynomials which are strongly coprime to all single variable Laurent polynomials. From this definition of coprimality we define the derived series localized at for a given sequence of multivariable polynomials . From such series we obtain refinements of the n–solvable filtration. The operation of infection by a string link is then used to demonstrate that for particular , certain quotients of successive terms of these refined filtrations have infinite rank.

Keywords
infection, string link, concordance
Mathematical Subject Classification 2010
Primary: 57M25
Secondary: 20J05
References
Publication
Received: 9 August 2011
Revised: 15 August 2013
Accepted: 20 August 2013
Published: 29 May 2014
Authors
John R Burke
Mathematics and Computer Science Department
Rhode Island College
600 Mount Pleasant Avenue
Providence, RI 02908-1991
USA