Torsion functions on moduli spaces in view of the cluster algebra

Takahiro Kitayama; Yuji Terashima

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arXiv · 1310.3068

Torsion functions on moduli spaces in view of the cluster algebra

Takahiro Kitayama·Yuji Terashima

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Abstract

We introduce non-acyclic $PGL_n(\mathbb{C})$-torsion of a 3-manifold with toroidal boundary as an extension of J. Porti's $PGL_2(\mathbb{C})$-torsion, and present an explicit formula of the $PGL_n(\mathbb{C})$-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.

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BibTeX RIS

Takahiro Kitayama, Yuji Terashima. 2014-11-11. Torsion functions on moduli spaces in view of the cluster algebra. https://arxiv.org/abs/1310.3068

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