Braids, complex volume and cluster algebras

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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.

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Hikami, K., & Inoue, R. (2015). Braids, complex volume and cluster algebras. Algebraic and Geometric Topology, 15(4), 2175–2194. https://doi.org/10.2140/agt.2015.15.2175

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