On simple loops on a solid torus of general genus
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- by Takeshi Kaneto
- Proc. Amer. Math. Soc. 86 (1982), 551-552
- DOI: https://doi.org/10.1090/S0002-9939-1982-0671234-5
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Abstract:
Let $l$ be a simple loop on the boundary of a solid torus $T$ of genus $g$. Let ${\mathbf {m}}$ be a complete system of oriented meridian disks of $T$. Let $W(l,{\mathbf {m}})$ be a word obtained by reading the intersections $l \cap {\mathbf {m}}$ along $l$. We shall give a natural method for realizing the cyclic reductions of $W(l,{\mathbf {m}})$ geometrically. This yields a simple proof of Whitehead-Zieschang’s theorem related to the minimality of the intersections of two systems $\{ {l_1}, \ldots ,{l_n}\}$ and ${\mathbf {m}}$.References
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Bibliographic Information
- © Copyright 1982 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 86 (1982), 551-552
- MSC: Primary 57N10; Secondary 57M05
- DOI: https://doi.org/10.1090/S0002-9939-1982-0671234-5
- MathSciNet review: 671234