Geodesic
Braids, complex volume and cluster algebras
Hikami, Kazuhiro1 ; Inoue, Rei2
1Faculty of Mathematics, Kyushu University, Fukuoka 819-0395, Japan
2Department of Mathematics and Informatics, Faculty of Science, Chiba University, Chiba 263-8522, Japan
Algebraic and Geometric Topology, Tome 15 (2015) no. 4, pp. 2175-2194
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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.

DOI : 10.2140/agt.2015.15.2175
Classification : 57M25, 13F60
Keywords: knot, hyperbolic volume, complex volume, cluster algebra

Hikami, Kazuhiro  1   ; Inoue, Rei  2

1 Faculty of Mathematics, Kyushu University, Fukuoka 819-0395, Japan
2 Department of Mathematics and Informatics, Faculty of Science, Chiba University, Chiba 263-8522, Japan 
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Hikami, Kazuhiro; Inoue, Rei. Braids, complex volume and cluster algebras. Algebraic and Geometric Topology, Tome 15 (2015) no. 4, pp. 2175-2194. doi: 10.2140/agt.2015.15.2175

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