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

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

 

Twist spinning revisited


Authors: Deborah L. Goldsmith and Louis H. Kauffman
Journal: Trans. Amer. Math. Soc. 239 (1978), 229-251
MSC: Primary 57Q45
MathSciNet review: 487047
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: This paper contains several applications of the following theorem: The 1-twist spin $ {L_1}(k)$ of any knot $ k \subset {S^{n - 1}}$ is interchangeable with the standard unknotted $ (n - 2)$-sphere K in $ {S^n}$ by means of a homeomorphism of triples $ h:({S^n},K,{L_1}(k)) \to ({S^n},{L_1}(k),K)$ which reverses the orientation of $ {S^n}$, and preserves the orientations of K and $ {L_1}(k)$. One of these applications is Zeeman's Theorem about twist spun knots; another is a proof of a conjecture of R. H. Fox about certain manifolds which have the same fundamental group.

We also prove that the iterated twist spun knot $ {L_{a,b}}(k) \subset {S^{n + 1}}$ is fiber equivalent to one of $ {L_{0,g}}(k)$ or $ {L_{g,g}}(k)$ where $ g = {\text{g.c.d.}}(a,b)$.


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


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 57Q45

Retrieve articles in all journals with MSC: 57Q45


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1978-0487047-7
PII: S 0002-9947(1978)0487047-7
Keywords: Manifold, knot, book structure, twist spinning
Article copyright: © Copyright 1978 American Mathematical Society