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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
Published electronically: May 19, 2009
MathSciNet review: 2515423
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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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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
Published electronically: 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.