Let Γ 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 = Γ\ Hn+1, under the assumption that H 1(X, Z) is infinite. Our results imply asymptotic equipartition of geodesics in distinct homology classes.
|Number of pages||13|
|State||Published - 2002|
Bibliographical noteFunding Information:
Jeffrey McGowan was supported in part by funds from the University of Kentucky Research Professorship program, and Peter Perry was supported in part by NSF grant DMS-9797051.
We would like to thank Charles Epstein and Rafe Mazzeo for several helpful conversations. Peter Perry gratefully acknowledges the support of the University of Kentucky’s research professorship program and Jeffrey McGowan thanks the University of Kentucky for hospitality during part of the time this work was done.
- Closed geodesics
- Hyperbolic manifolds
- Selberg trace formula
ASJC Scopus subject areas
- Geometry and Topology