Volume 13, issue 5 (2013)

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

Volume 17
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
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Author Index
To Appear
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Slice knots which bound punctured Klein bottles

Arunima Ray

Algebraic & Geometric Topology 13 (2013) 2713–2731

We investigate the properties of knots in S3 which bound punctured Klein bottles, such that a pushoff of the knot has zero linking number with the knot, ie has zero framing. This is motivated by the many results in the literature regarding slice knots of genus one, for example, the existence of homologically essential zero self-linking simple closed curves on genus one Seifert surfaces for algebraically slice knots. Given a knot K bounding a punctured Klein bottle F with zero framing, we show that J, the core of the orientation preserving band in any disk–band form of F, has zero self-linking. We prove that such a K is slice in a [12]–homology B4 if and only if J is as well, a stronger result than what is currently known for genus one slice knots. As an application, we prove that given knots K and J and any odd integer p, the (2,p)–cables of K and J are [12]–concordant if and only if K and J are [12]–concordant. In particular, if the (2,1)–cable of a knot K is slice, K is slice in a [12]–homology ball.

knot concordance
Mathematical Subject Classification 2010
Primary: 57M25
Received: 14 March 2013
Revised: 15 March 2013
Accepted: 17 March 2013
Published: 10 July 2013
Arunima Ray
Department of Mathematics
Rice University
MS-136, PO Box-1892
Houston, TX 77251-1892