Growth of conjugacy classes of Schottky groups in higher rank symmetric spaces
classification
🧮 math.DG
math.GR
keywords
symmetricgammaschottkyasymptoticaxialclassesclosedconjugacy
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Let $X$ be a globally symmetric space of noncompact type, and $\Gamma\subset\Isom(X)$ a Schottky group of axial isometries. Then $M:=X/\Gamma$ 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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