Braids, Complex Volume, and Cluster Algebra
Geometric Topology
2015-09-30 v6 Mathematical Physics
math.MP
Abstract
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.
Cite
@article{arxiv.1304.4776,
title = {Braids, Complex Volume, and Cluster Algebra},
author = {Kazuhiro Hikami and Rei Inoue},
journal= {arXiv preprint arXiv:1304.4776},
year = {2015}
}
Comments
18 pages