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Spectral geometry, link complements and surgery diagrams

Abstract:

We provide an upper bound on the Cheeger constant and first eigenvalue of the Laplacian of a finite-volume hyperbolic 3-manifold M, in terms of data from any surgery diagram for M. This has several consequences. We prove that a family of hyperbolic alternating link complements is expanding if and only if they have bounded volume. We also provide examples of hyperbolic 3-manifolds which require 'complicated' surgery diagrams, thereby proving that a recent theorem of Constantino and Thurston is...

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Publication status:
Published

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Publisher copy:
10.1007/s10711-009-9451-5

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
Journal:
GEOMETRIAE DEDICATA
Volume:
147
Issue:
1
Pages:
191-206
Publication date:
2008-10-29
DOI:
EISSN:
1572-9168
ISSN:
0046-5755
Source identifiers:
65967
Language:
English
Keywords:
Pubs id:
pubs:65967
UUID:
uuid:6f5d01a6-ca90-447a-b91e-974579e206a0
Local pid:
pubs:65967
Deposit date:
2012-12-19

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