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Dehn Fillings of Knot Manifolds Containing Essential Twice-Punctured Tori.
・ISBN 978-1-4704-6870-5 paper US$ 85.00
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| 著者・編者 | Boyer, Steven / Gordon, Cameron McA. / Zhang, Xingru, |
|---|---|
| シリーズ | Memoirs of the American Mathematical Society |
| 出版社 | (American Mathematical Society, US) |
| 出版年月 | 2024 |
| ページ数 | 106 pp. |
| 言語 | ENG |
| ニュース番号 | ＜M25-7732＞ |
解説
We show that if a hyperbolic knot manifold M contains an essential twicepunctured torus F with boundary slope ? and admits a filling with slope ? producing a Seifert fibred space, then the distance between the slopes ? and ? is less than or equal to 5 unless M is the exterior of the figure eight knot. The result is sharp; the bound of 5 can be realized on infinitely many hyperbolic knot manifolds. We also determine distance bounds in the case that the fundamental group of the ?-filling contains no non-abelian free group. The proofs are divided into the four cases F is a semi-fibre, F is a fibre, F is non-separating but not a fibre, and F is separating but not a semi-fibre, and we obtain refined bounds in each case.