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The complex volumes of twist knots
Authors:
Jinseok Cho, Jun Murakami and Yoshiyuki Yokota
Journal:
Proc. Amer. Math. Soc. 137 (2009), 3533-3541
MSC (2000):
Primary 57M27; Secondary 51M25, 58J28
Posted:
May 19, 2009
MathSciNet review:
2515423
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Additional Information
Abstract: For a given hyperbolic knot, the third author defined a function whose imaginary part gives the hyperbolic volume of the knot complement. We show that, for a twist knot, the function actually gives the complex volume of the knot complement using Zickert's and Neumann's theory of the extended Bloch groups and the complex volumes.
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- H. Murakami, Kashaev's invariant and the volume of a hyperbolic knot after Y. Yokota, Physics and combinatorics 1999 (Nagoya), 244-272, World Sci. Publ., River Edge, NJ, 2001. MR 1865040 (2002k:57031)
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Additional Information
Jinseok Cho
Affiliation:
Department of Mathematical Sciences, Seoul National University, Seoul 151-742, Korea
Email:
jindol@math.snu.ac.kr
Jun Murakami
Affiliation:
Department of Mathematics, Faculty of Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan
Email:
murakami@waseda.jp
Yoshiyuki Yokota
Affiliation:
Department of Mathematics, Tokyo Metropolitan University, Tokyo 192-0397, Japan
Email:
jojo@tmu.ac.jp
DOI:
http://dx.doi.org/10.1090/S0002-9939-09-09906-7
PII:
S 0002-9939(09)09906-7
Keywords:
Twist knot,
volume conjecture,
complex volume
Received by editor(s):
December 29, 2008
Posted:
May 19, 2009
Additional Notes:
This work was carried out while the first author was visiting Waseda University with the support of the Korea National Foundation Grant funded by the Korean Government (MOEHRD) (KRF-2007-612-C00037)
Communicated by:
Daniel Ruberman
Article copyright:
© Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
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