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Transactions of the American Mathematical Society
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
MathSciNet review: 0275412
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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.

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Additional Information

PII: S 0002-9947(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

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