Simple knots without unique minimal surfaces

Lyon, Herbert C.

doi:10.1090/S0002-9939-1974-0377850-8

Simple knots without unique minimal surfaces
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by Herbert C. Lyon

Proc. Amer. Math. Soc. 43 (1974), 449-454

DOI: https://doi.org/10.1090/S0002-9939-1974-0377850-8

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Abstract:

We construct infinitely many simple knots and infinitely many nonsimple knots, all of genus one, and all having both knotted and unknotted minimal spanning surfaces. The complements of the simple knots all contain closed incompressible surfaces of genus two.

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