The analytic torsion and its asymptotic behaviour for sequences of\n hyperbolic manifolds of finite volume

2013/07/18 by Werner Mueller, Mueller, Werner, Jonathan Pfaff +1
Mathematics · #58J52 #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Representation Theory (math.RT) #Spectral Theory (math.SP)

paper · pdf · doi:10.48550/arxiv.1307.4914

openalex publication_date 2013/07/18 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

In this paper we study the regularized analytic torsion of finite volume\nhyperbolic manifolds. We consider sequences of coverings X_i of a fixed\nhyperbolic orbifold X₀. Our main result is that for certain sequences of\ncoverings and strongly acyclic flat bundles, the analytic torsion divided by\nthe index of the covering, converges to the L²-torsion. Our results apply to\ncertain sequences of arithmetic groups, in particular to sequences of principal\ncongruence subgroups of SO⁰(d,1)( Z) and to sequences of principal\ncongruence subgroups or Hecke subgroups of Bianchi groups.\n

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