Generalized unknotting operations and tangle decompositions
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- by Tsuyoshi Kobayashi PDF
- Proc. Amer. Math. Soc. 105 (1989), 471-478 Request permission
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.References
- Martin Scharlemann, Sutured manifolds and generalized Thurston norms, J. Differential Geom. 29 (1989), no. 3, 557–614. MR 992331
- Martin Scharlemann and Abigail Thompson, Unknotting number, genus, and companion tori, Math. Ann. 280 (1988), no. 2, 191–205. MR 929535, DOI 10.1007/BF01456051
Additional Information
- © Copyright 1989 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 105 (1989), 471-478
- MSC: Primary 57M25; Secondary 57N10
- DOI: https://doi.org/10.1090/S0002-9939-1989-0977926-9
- MathSciNet review: 977926