Cluster variables, ancestral triangles and Alexander polynomials
Geometric Topology
2019-03-26 v2 Mathematical Physics
Combinatorics
math.MP
Abstract
In this paper, we show that Alexander polynomials for any 2-bridge knots are specializations of cluster variables. A key tool is an ancestral triangle which appeared in both quantum topology and hyperbolic geometry in different ways.
Cite
@article{arxiv.1812.02434,
title = {Cluster variables, ancestral triangles and Alexander polynomials},
author = {Wataru Nagai and Yuji Terashima},
journal= {arXiv preprint arXiv:1812.02434},
year = {2019}
}
Comments
33 pages: typos corrected, detailed examples added in section 4