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Transactions of the American Mathematical Society

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



Knots with infinitely many minimal spanning surfaces

Author: Julian R. Eisner
Journal: Trans. Amer. Math. Soc. 229 (1977), 329-349
MSC: Primary 55A25
Addendum: Trans. Amer. Math. Soc. 233 (1977), 367-369.
MathSciNet review: 0440528
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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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Keywords: Knot, fibered knot, composite knot, simple knot, minimal spanning surface, isotopic deformation, infinite cyclic covering space, free product with amalgamation
Article copyright: © Copyright 1977 American Mathematical Society