Torsion functions on moduli spaces in view of the cluster algebra

Abstract

We introduce non-acyclic $PG{L}_n(\mathbb{C})$-torsion of a 3-manifold with toroidal boundary as an extension of J. Porti's $PG{L}_2(\mathbb{C})$-torsion, and present an explicit formula of the $PG{L}_n(\mathbb{C})$-torsion of a mapping torus for a surface with punctures, by using the higher Teichmüler theory due to V. Fock and A. Goncharov. Our formula gives a concrete rational function which represents the torsion function and comes from a concrete cluster transformation associated with the mapping class.

17 pages, 2 figures; 19 pages, 2 figures, to appear in Geometriae Dedicata

References in corpus (2)

• Hyperbolic 3-manifolds and Cluster Algebras
• Local coordinates for SL(n,C) character varieties of finite volume hyperbolic 3-manifolds