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HYPERBOLIC 3-MANIFOLDS AND CLUSTER ALGEBRAS
Published online by Cambridge University Press: 28 September 2017
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.
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- © 2017 Foundation Nagoya Mathematical Journal
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