Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Incompressible surfaces in knot spaces


Author: Herbert C. Lyon
Journal: Trans. Amer. Math. Soc. 157 (1971), 53-62
MSC: Primary 55.20
DOI: https://doi.org/10.1090/S0002-9947-1971-0275412-6
MathSciNet review: 0275412
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The following theorems are proved.

Theorem 1. There exist infinitely many distinct, prime, Neuwirth knots, each of which has the property that its complement contains closed, incompressible surfaces of arbitrarily high genus.

Theorem 2. There exists a genus one knot which has incompressible spanning surfaces of arbitrarily high genus.


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


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 55.20

Retrieve articles in all journals with MSC: 55.20


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1971-0275412-6
Keywords: Closed surface, genus, incompressible surface, knot, knot space, Neuwirth knot, prime knot, spanning surface
Article copyright: © Copyright 1971 American Mathematical Society