### 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 |
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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 1 |

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

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## Cite this

Cho, J., Murakami, J., & Yokota, Y. (2009). The complex volumes of twist knots.

*Proceedings of the American Mathematical Society*,*137*(10), 3533-3541. https://doi.org/10.1090/S0002-9939-09-09906-7