Dehn Fillings of Knot Manifolds Containing Essential Twice-Punctured Tori

Language: English

Published by American Mathematical Society, US, 2024

1470468700 / 9781470468705

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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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Bibliographic details

Title
Dehn Fillings of Knot Manifolds Containing Essential Twice-Punctured Tori
Author
Steven Boyer, Cameron McA. Gordon, Xingru Zhang
Publisher
American Mathematical Society, US
Publication year
2024
Condition
New
Binding
Paperback
Language
English
ISBN 10
1470468700
ISBN 13
9781470468705
Item weight
272 grams

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