Growth of conjugacy classes of Schottky groups in higher rank symmetric spaces

2005/12/14 by Gabriele Link, Link, Gabriele
Mathematics · #22E40 #53C22 #53C35 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #Group Theory (math.GR) #math.DG #math.GR #msc:22E40 #msc:53C22 #msc:53C35

paper · pdf · doi:10.48550/arxiv.math/0512333

15 pages

arxiv created 2005/12/14 · openalex publication_date 2005/12/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let X be a globally symmetric space of noncompact type, and Γ⊂\Isom(X) a Schottky group of axial isometries. Then M:=X/Γ is a locally symmetric Riemannian manifold of infinite volume. The goal of this note is to give an asymptotic estimate for the number of primitive closed geodesics in M modulo free homotopy with period less than t.

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