Torsion functions on moduli spaces in view of the cluster algebra

Takahiro Kitayama; Yuji Terashima

doi:10.1007/s10711-014-0032-x

Torsion functions on moduli spaces in view of the cluster algebra

Takahiro Kitayama, Yuji Terashima

SCI - Mathematics

Tokyo Institute of Technology

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

We introduce non-acyclic PGLn(C)-torsion of a 3-manifold with toroidal boundary as an extension of J. Porti’s PGL2(C)-torsion, and present an explicit formula of the PGLn(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.

Original language	English
Pages (from-to)	125-143
Number of pages	19
Journal	Geometriae Dedicata
Volume	175
Issue number	1
DOIs	https://doi.org/10.1007/s10711-014-0032-x
Publication status	Published - 2015 Apr 1

Keywords

Cluster algebra
Representation space
Torsion invariant

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abstract = "We introduce non-acyclic PGLn(C)-torsion of a 3-manifold with toroidal boundary as an extension of J. Porti{\textquoteright}s PGL2(C)-torsion, and present an explicit formula of the PGLn(C)-torsion of a mapping torus for a surface with punctures, by using the higher Teichm{\"u}ler 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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AU - Terashima, Yuji

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N2 - We introduce non-acyclic PGLn(C)-torsion of a 3-manifold with toroidal boundary as an extension of J. Porti’s PGL2(C)-torsion, and present an explicit formula of the PGLn(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.

AB - We introduce non-acyclic PGLn(C)-torsion of a 3-manifold with toroidal boundary as an extension of J. Porti’s PGL2(C)-torsion, and present an explicit formula of the PGLn(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.

KW - Cluster algebra

KW - Representation space

KW - Torsion invariant

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Torsion functions on moduli spaces in view of the cluster algebra

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Keywords

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