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Dehn Fillings of Knot Manifolds Containing Essential Twice-Punctured Tori

By (author) Steven Boyer, By (author) Cameron McA. Gordon, By (author) 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.

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Normally shipped | Enquiries only
Publisher | American Mathematical Society
Published date | 31 May 2024
Language |
Format | Paperback / softback
Pages | 106
Dimensions | 254 x 178 x 0mm (L x W x H)
Weight | 272g
ISBN | 978-1-4704-6870-5
Readership Age |
BISAC | mathematics / geometry / general


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