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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


Generalized unknotting operations and tangle decompositions

Author: Tsuyoshi Kobayashi
Journal: Proc. Amer. Math. Soc. 105 (1989), 471-478
MSC: Primary 57M25; Secondary 57N10
MathSciNet review: 977926
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Abstract: Suppose that a knot $ {K_L}$ in $ {S^3}$ is obtained from a knot $ K$ by an $ n$-parallel ($ n$-antiparallel resp.) crossing change. Let $ T$ be an incompressible, $ \partial $-incompressible surface properly embedded in $ {S^3} - \dot N(K)$ with $ \partial T$ a union of meridian loops and $ \chi (T) > p(1 - 2n)$, for some $ p$ . We show that either $ T$ is isotoped to intersect $ L$ in $ \leq 2p - 2$ points, or there is a minimal genus Seifert surface for $ {K_L}$ intersecting the corresponding crossing link in two ($ \leq 2$ resp.) points.

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PII: S 0002-9939(1989)0977926-9
Keywords: Knot, unknotting operation, tangle, sutured manifold
Article copyright: © Copyright 1989 American Mathematical Society