The complex volumes of twist knots

Cho, Jinseok; Murakami, Jun; Yokota, Yoshiyuki

doi:10.1090/S0002-9939-09-09906-7

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.

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