Dehn fillings of knot manifolds containing essential twice-punctured tori
Summary: We show that if a hyperbolic knot manifold M contains an essential twice-punctured torus F with boundary slope β and admits a filling with slope α producing a Seifert fibred space, then the distance between the slopes α and β is less than or equal to 5 unless M is the exterior of the figure...
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| Format: | UnknownFormat |
| Sprache: | eng |
| Veröffentlicht: |
Providence, RI
American Mathematical Society
March 2024
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| Schriftenreihe: | Memoirs of the American Mathematical Society
volume 295, number 1469 (March 2024) |
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| Online Zugang: | Inhaltsverzeichnis zbMATH |
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Tag hinzufügen | Zusammenfassung: | Summary: We show that if a hyperbolic knot manifold M contains an essential twice-punctured torus F with boundary slope β and admits a filling with slope α producing a Seifert fibred space, then the distance between the slopes α and β 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 α-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. |
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| Beschreibung: | Description based on publisher supplied metadata and other sources "Mach 2024, volume 295, number 1469 (first of 6 numbers)" |
| Beschreibung: | v, 123 Seiten |
| ISBN: | 9781470468705 978-1-4704-6870-5 |