The asymptotic behavior of the Reidemeister torsion for Seifert manifolds and PSL(2;R)-representations of Fuchsian groups

2014/10/11 by Yoshikazu Yamaguchi, Yamaguchi, Yoshikazu
Mathematics · #57M05 (primary) 57M50 (secondary) #57M27 #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.GT #msc:57M05 #msc:57M27 #msc:57M50

paper · pdf · doi:10.48550/arxiv.1410.2970

12 pages

arxiv created 2014/10/11 · openalex publication_date 2014/10/11 · arxiv updated 2014/10/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that a PSL(2;R)-representation of a Fuchsian group induces the asymptotics of the Reidemeister torsion for the Seifert manifold corresponding to the euler class of the PSL(2;R)-representation. We also show that the limit of leading coefficient of the Reidemeister torsion is determined by the euler class of a PSL(2;R)-representation of a Fuchsian group. In particular, the leading coefficient of the Reidemeister torsion for the unit tangent bundle over a two-orbifold converges to -χlog2 where χ is the Euler characteristic of the two-orbifold. We also give a relation between ℤ₂-extensions for PSL(2;R)-representations of a Fuchsian group and the asymptotics of the Reidemeister torsion.

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