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Transactions of the American Mathematical Society

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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.


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

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Additional Information

DOI: http://dx.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