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The volume of hyperbolic alternating link complements

Abstract:

If a hyperbolic link has a prime alternating diagram D, then we show that the link complement's volume can be estimated directly from D. We define a very elementary invariant of the diagram D, its twist number t(D), and show that the volume lies between v_3(t(D) - 2)/2 and v_3(16t(D) - 16), where v_3 is the volume of a regular hyperbolic ideal 3-simplex. As a consequence, the set of all hyperbolic alternating and augmented alternating link complements is a closed subset of the space of all co...

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Publication status:
Published

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Publisher copy:
10.1112/S0024611503014291

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Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Inst
Journal:
PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY
Volume:
88
Issue:
1
Pages:
204-224
Publication date:
2000-12-19
DOI:
EISSN:
1460-244X
ISSN:
0024-6115
URN:
uuid:ce655740-f427-4ef0-96df-ceeec5abc762
Source identifiers:
26536
Local pid:
pubs:26536
Language:
English
Keywords:

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