Knots with infinitely many minimal spanning surfaces

Eisner, Julian R.

doi:10.1090/S0002-9947-1977-0440528-3

Knots with infinitely many minimal spanning surfaces
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by Julian R. Eisner PDF

Trans. Amer. Math. Soc. 229 (1977), 329-349 Request permission

Addendum: Trans. Amer. Math. Soc. 233 (1977), 367-369.

Abstract:

We show that if ${k_1}$ and ${k_2}$ are nonfibered knots, then the composite knot $K = {k_1}\# {k_2}$ has an infinite collection of minimal spanning surfaces, no two of which are isotopic by an isotopy which leaves the knot K fixed. This result is then applied to show that whether or not a knot has a unique minimal spanning surface can depend on what definition of spanning surface equivalence is used.

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