The complex volumes of twist knots
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- by Jinseok Cho, Jun Murakami and Yoshiyuki Yokota PDF
- Proc. Amer. Math. Soc. 137 (2009), 3533-3541 Request permission
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.References
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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
- MR Author ID: 249930
- Email: murakami@waseda.jp
- Yoshiyuki Yokota
- Affiliation: Department of Mathematics, Tokyo Metropolitan University, Tokyo 192-0397, Japan
- MR Author ID: 292071
- Email: jojo@tmu.ac.jp
- 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
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 137 (2009), 3533-3541
- MSC (2000): Primary 57M27; Secondary 51M25, 58J28
- DOI: https://doi.org/10.1090/S0002-9939-09-09906-7
- MathSciNet review: 2515423