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Search: id:A156057
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| A156057 |
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Decimal expansion of log(3)/2. |
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+0
2
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| 5, 4, 9, 3, 0, 6, 1, 4, 4, 3, 3, 4, 0, 5, 4, 8, 4, 5, 6, 9, 7, 6, 2, 2, 6, 1, 8, 4, 6, 1, 2, 6, 2, 8, 5, 2, 3, 2, 3, 7, 4, 5, 2, 7, 8, 9, 1, 1, 3, 7, 4, 7, 2, 5, 8, 6, 7, 3, 4, 7, 1, 6, 6, 8, 1, 8, 7, 4, 7, 1, 4, 6, 6, 0, 9, 3, 0, 4, 4, 8, 3, 4, 3, 6, 8, 0, 7, 8, 7, 7, 4, 0, 6, 8, 6, 6, 0, 4, 4
(list; cons; graph; listen)
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OFFSET
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1,1
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COMMENT
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Culler and Shalen abstract: We give lower bounds on the maximal injectivity radius for a closed orientable hyperbolic 3-manifold M with first Betti number 2, under some additional topological hypotheses. A corollary of the main result is that if M has first Betti number 2 and contains no fibroid surface then its maximal injectivity radius exceeds 0.32798. For comparison, Andrew Przeworski showed, with no topological restrictions, that the maximal injectivity radius exceeds arcsinh(1/4) = 0.247..., while the authors showed that if M has first Betti number at least 3 then the maximal injectivity exceeds log(3)/2 = 0.549.... The proof combines a result due to Przeworski with techniques developed by the authors in the 1990s.
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LINKS
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Marc Culler, Peter B. Shalen, Betti numbers and injectivity radii,
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CROSSREFS
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Cf. A002391 = decimal expansion of natural logarithm of 3.
Sequence in context: A090124 A097943 A077142 this_sequence A125057 A021186 A092302
Adjacent sequences: A156054 A156055 A156056 this_sequence A156058 A156059 A156060
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KEYWORD
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cons,easy,nonn
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), Feb 03 2009
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EXTENSIONS
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All digits were wrong. Corrected by N. J. A. Sloane (njas(AT)research.att.com), Feb 05 2009
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