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

Remote Access
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)


Nonsimple, ribbon fibered knots

Author: Katura Miyazaki
Journal: Trans. Amer. Math. Soc. 341 (1994), 1-44
MSC: Primary 57M25
MathSciNet review: 1176509
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The connected sum of an arbitrary knot and its mirror image is a ribbon knot, however the converse is not necessarily true for all ribbon knots. We prove that the converse holds for any ribbon fibered knot which is a connected sum of iterated torus knots, knots with irreducible Alexander polynomials, or cables of such knots. This gives a practical method to detect nonribbon fibered knots. The proof uses a characterization of homotopically ribbon, fibered knots by their monodromies due to Casson and Gordon. We also study when cable fibered knots are ribbon and results which support the following conjecture.

Conjecture. If a $ (p,q)$ cable of a fibered knot $ k$ is ribbon where $ p(> 1)$ is the winding number of a cable in $ {S^1} \times {D^2}$, then $ q = \pm 1$ and $ k$ is ribbon.

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

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 57M25

Retrieve articles in all journals with MSC: 57M25

Additional Information

PII: S 0002-9947(1994)1176509-4
Keywords: Ribbon, homotopically ribbon, fibered knot, monodromy, Johannson's characteristic submanifold
Article copyright: © Copyright 1994 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