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Braids, Complex Volume, and Cluster Algebra

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

preprint2014arXivOpen access
Kazuhiro HikamiRei Inoue
math-phmath.GTmath.MP
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Kazuhiro HikamiRei Inoue

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