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Closed Geodesics in Homology Classes for Convex Co-Compact Hyperbolic Manifolds

Authors:	Jeffrey McGowan Peter Perry

Affiliation:	(1) Department of Mathematics, Central Connecticut State University, New Britain, CT, 06050, U.S.A.;(2) Present address: Department of Mathematics, University of Kentucky, Lexington, KY, 40506–0027, U.S.A.;(3) Department of Mathematics, University of Kentucky, Lexington, KY, 40506–0027, U.S.A.

Abstract:	Let be a convex co-compact, torsion-free, discrete group of isometries of real hyperbolic space Hⁿ⁺¹. We compute the asymptotics of the counting function for closed geodesics in homology classes for the quotient manifold X = Hⁿ⁺¹, under the assumption that H¹(X, Z) is infinite. Our results imply asymptotic equipartition of geodesics in distinct homology classes.

Keywords:	closed geodesics hyperbolic manifolds Selberg trace formula
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