Torsion functions on moduli spaces in view of the cluster algebra

Takahiro Kitayama, Yuji Terashima

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


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 languageEnglish
Pages (from-to)125-143
Number of pages19
JournalGeometriae Dedicata
Issue number1
Publication statusPublished - 2015 Apr 1


  • Cluster algebra
  • Representation space
  • Torsion invariant


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