Dehn Fillings of Knot Manifolds Containing Essential Twice-Punctured Tori
Author(s)
Bibliographic Information
Dehn Fillings of Knot Manifolds Containing Essential Twice-Punctured Tori
（Memoirs of the American Mathematical Society, no. 1469）
American Mathematical Society, c.2024
- : [pbk.]
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Note
"March 2024, volume 295, number 1469 (first of 6 numbers)"
Includes bibliographical references (p. 121-123)
Description and Table of Contents
Description
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.
Table of Contents
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
by "Nielsen BookData"
