Hyperbolic 3-manifolds and Cluster Algebras
Geometric Topology
2019-07-31 v2 High Energy Physics - Theory
Rings and Algebras
Abstract
We advocate the use of cluster algebras and their y-variables in the study of hyperbolic 3-manifolds. We study hyperbolic structures on the mapping tori of pseudo-Anosov mapping classes of punctured surfaces, and show that cluster y-variables naturally give the solutions of the edge-gluing conditions of ideal tetrahedra. We also comment on the completeness of hyperbolic structures.
Cite
@article{arxiv.1112.3106,
title = {Hyperbolic 3-manifolds and Cluster Algebras},
author = {Kentaro Nagao and Yuji Terashima and Masahito Yamazaki},
journal= {arXiv preprint arXiv:1112.3106},
year = {2019}
}
Comments
v2: 26 pages, 17 figures