Hyperbolic 3-manifolds and Cluster Algebras

Details Hyperbolic 3-manifolds and Cluster Algebras Hyperbolic 3-manifolds and Cluster Algebras

2011-12-14

arxiv.org/abs/1112.3106v1

Mathematics

Geometric Topology

29 pages, 18 figures

Scientific paper

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.

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