Dehn Fillings of Knot Manifolds Containing Essential Twice-Punctured Tori

著者

    • Boyer, Steve
    • Gordon, Cameron McA.
    • Zhang, Xingru

書誌事項

Dehn Fillings of Knot Manifolds Containing Essential Twice-Punctured Tori

Steve Boyer, Cameron McA. Gordon, Xingru Zhang

(Memoirs of the American Mathematical Society, no. 1469)

American Mathematical Society, c.2024

  • : [pbk.]

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注記

"March 2024, volume 295, number 1469 (first of 6 numbers)"

Includes bibliographical references (p. 121-123)

内容説明・目次

内容説明

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.

目次

Chapters 1. Introduction 2. Examples 3. Proof of Theorems and 4. Initial assumptions and reductions 5. Culler-Shalen theory 6. Bending characters of triangle group amalgams 7. The proof of Theorem when $F$ is a semi-fibre 8. The proof of Theorem when $F$ is a fibre 9. Further assumptions, reductions, and background material 10. The proof of Theorem when $F$ is non-separating but not a fibre 11. Algebraic and embedded $n$-gons in $X^\epsilon $ 12. The proof of Theorem when $F$ separates but is not a semi-fibre and $t_1^+ + t_1^- > 0$ 13. Background for the proof of Theorem when $F$ separates and $t_1^+ = t_1^-=0$ 14. Recognizing the figure eight knot exterior 15. Completion of the proof of Theorem when $\Delta (\alpha , \beta ) \geq 7$ 16. Completion of the proof of Theorem when $X^-$ is not a twisted $I$-bundle 17. Completion of the proof of Theorem when ${\Delta }(\alpha ,\beta )=6$ and $d = 1$ 18. The case that $F$ separates but not a semi-fibre, $t_1^+ = t_1^- = 0$, $d \ne 1$, and $M(\alpha )$ is very small 19. The case that $F$ separates but is not a semi-fibre, $t_1^+ = t_1^- = 0$, $d>1$, and $M(\alpha )$ is not very small 20. Proof of Theorem

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詳細情報

  • NII書誌ID(NCID)
    BD07088322
  • ISBN
    • 9781470468705
  • 出版国コード
    us
  • タイトル言語コード
    eng
  • 本文言語コード
    eng
  • 出版地
    Providence, RI
  • ページ数/冊数
    v, 123 p.
  • 大きさ
    26 cm
  • 親書誌ID
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