Vetenskap & teknik
Pocket
Dehn Fillings of Knot Manifolds Containing Essential Twice-Punctured Tori
Steven Boyer • Cameron Mca Gordon • Xingru Zhang
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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.
- Format: Pocket/Paperback
- ISBN: 9781470468705
- Språk: Engelska
- Antal sidor: 106
- Utgivningsdatum: 2024-05-31
- Förlag: American Mathematical Society