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ON THE COMPLEX VOLUME OF HYPERBOLIC KNOTS

YOSHIYUKI YOKOTA

Department of Mathematics and Information Sciences, Tokyo Metropolitan University, Hachioji, Tokyo 192-0397, Japan

https://doi.org/10.1142/S021821651100908XCited by:19 (Source: Crossref)

Abstract

In this paper, we give a formula of the complex volumes of hyperbolic knot complements, which is related to the volume conjecture for hyperbolic knots.

Keywords:

AMSC: 57M27, 57M50

References

J. Cho, J. Murakami and Y. Yokota, Proc. Amer. Math. Soc. 137, 3533 (2009), DOI: 10.1090/S0002-9939-09-09906-7. Crossref, Web of Science, Google Scholar
R. Kashaev, Lett. Math. Phys. 39, 269 (1997), DOI: 10.1023/A:1007364912784. Crossref, Web of Science, Google Scholar
R. Meyerhoff, Low-Dimensional Topology and Kleinian Groups, London Mathematical Society Lecture Note Series 112 (Cambridge University Press, 1986) pp. 217–239. Google Scholar
H. Murakami and J. Murakami, Acta Math. 186, 85 (2001), DOI: 10.1007/BF02392716. Crossref, Web of Science, Google Scholar
H. Murakami, J. Murakami, M. Okamoto, T. Takata and Y. Yokota, On Kashaev's conjecture for hyperbolic knots and links, preprint . Google Scholar
W. Neumann, Geom. Topol. 8, 413 (2004), DOI: 10.2140/gt.2004.8.413. Crossref, Web of Science, Google Scholar
W. Neumann and D. Zagier, Topology 24, 307 (1985), DOI: 10.1016/0040-9383(85)90004-7. Crossref, Web of Science, Google Scholar
J. Weeks, Handbook of Knot Theory (Elsevier, Amsterdam, 2005) pp. 461–480. Crossref, Google Scholar
Y. Yokota, On the volume conjecture for hyperbolic knots, preprint , arXiv:math/0009165 . Google Scholar
C. Zickert, Duke Math. J. 150, 489 (2009), DOI: 10.1215/00127094-2009-058. Crossref, Web of Science, Google Scholar