Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


New examples of non-slice, algebraically slice knots

Author: Charles Livingston
Journal: Proc. Amer. Math. Soc. 130 (2002), 1551-1555
MSC (1991): Primary 57M25, 57N70, 57Q60
Published electronically: October 12, 2001
MathSciNet review: 1879982
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: For $n >1$, if the Seifert form of a knotted $2n-1$-sphere $K$ in $S^{2n+ 1}$has a metabolizer, then the knot is slice. Casson and Gordon proved that this is false in dimension three. However, in the three-dimensional case it is true that if the metabolizer has a basis represented by a strongly slice link, then $K$ is slice. The question has been asked as to whether it is sufficient that each basis element is represented by a slice knot to assure that $K$ is slice. For genus one knots this is of course true; here we present genus two counterexamples.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 57M25, 57N70, 57Q60

Retrieve articles in all journals with MSC (1991): 57M25, 57N70, 57Q60

Additional Information

Charles Livingston
Affiliation: Department of Mathematics, Indiana University, Bloomington, Indiana 47405

PII: S 0002-9939(01)06201-3
Keywords: Knot concordance, algebraically slice
Received by editor(s): August 10, 2000
Received by editor(s) in revised form: November 10, 2000
Published electronically: October 12, 2001
Communicated by: Ronald A. Fintushel
Article copyright: © Copyright 2001 American Mathematical Society

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia