### 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.

Original language | English |
---|---|

Pages (from-to) | 3533-3541 |

Number of pages | 9 |

Journal | Proceedings of the American Mathematical Society |

Volume | 137 |

Issue number | 10 |

DOIs | |

Publication status | Published - 2009 Oct |

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### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Proceedings of the American Mathematical Society*,

*137*(10), 3533-3541. https://doi.org/10.1090/S0002-9939-09-09906-7

**The complex volumes of twist knots.** / Cho, Jinseok; Murakami, Jun; Yokota, Yoshiyuki.

Research output: Contribution to journal › Article

*Proceedings of the American Mathematical Society*, vol. 137, no. 10, pp. 3533-3541. https://doi.org/10.1090/S0002-9939-09-09906-7

}

TY - JOUR

T1 - The complex volumes of twist knots

AU - Cho, Jinseok

AU - Murakami, Jun

AU - Yokota, Yoshiyuki

PY - 2009/10

Y1 - 2009/10

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=77951028144&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77951028144&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-09-09906-7

DO - 10.1090/S0002-9939-09-09906-7

M3 - Article

AN - SCOPUS:77951028144

VL - 137

SP - 3533

EP - 3541

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 10

ER -