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Transactions of the American Mathematical Society
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}\char93 {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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1977-0440528-3
PII: S 0002-9947(1977)0440528-3
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