#### Volume 15, issue 4 (2015)

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Braids, complex volume and cluster algebras

### Kazuhiro Hikami and Rei Inoue

Algebraic & Geometric Topology 15 (2015) 2175–2194
##### Abstract

We try to give a cluster-algebraic interpretation of the complex volume of knots. We construct the $R$–operator from cluster mutations, and show that it can be regarded as a hyperbolic octahedron. The cluster variables are interpreted as the edge parameters used by Zickert for computing complex volume.

##### Keywords
knot, hyperbolic volume, complex volume, cluster algebra
Primary: 57M25
Secondary: 13F60
##### Publication
Received: 28 April 2014
Revised: 6 November 2014
Accepted: 14 November 2014
Published: 10 September 2015
##### Authors
 Kazuhiro Hikami Faculty of Mathematics Kyushu University Fukuoka 819-0395 Japan Rei Inoue Department of Mathematics and Informatics, Faculty of Science Chiba University Chiba 263-8522 Japan