Closed geodesics in homology classes for convex co-compact hyperbolic manifolds

Jeffrey McGowan, Peter Perry

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


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.

Original languageEnglish
Pages (from-to)197-209
Number of pages13
JournalGeometriae Dedicata
Issue number1
StatePublished - 2002

Bibliographical note

Funding 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.

Funding Information:
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


Dive into the research topics of 'Closed geodesics in homology classes for convex co-compact hyperbolic manifolds'. Together they form a unique fingerprint.

Cite this