A Generalization of the prime geodesic theorem to counting conjugacy classes of free subgroups

@article{Bowen2006AGO,
  title={A Generalization of the prime geodesic theorem to counting conjugacy classes of free subgroups},
  author={L. Bowen},
  journal={Geometriae Dedicata},
  year={2006},
  volume={124},
  pages={37-67}
}
  • L. Bowen
  • Published 2006
  • Mathematics
  • Geometriae Dedicata
The classical prime geodesic theorem (PGT) gives an asymptotic formula (as x tends to infinity) for the number of closed geodesics with length at most x on a hyperbolic manifold M. Closed geodesics correspond to conjugacy classes of π1(M) = Γ where Γ is a lattice in G = SO(n,1). The theorem can be rephrased in the following format. Let $$X(\mathbb{Z},\Gamma)$$ be the space of representations of $$\mathbb{Z}$$ into Γ modulo conjugation by Γ. $$X(\mathbb{Z},G)$$ is defined similarly. Let $$\pi… Expand

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