Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Generalization of the Prime Geodesic Theorem to Counting Conjugacy
  Classes of Free Subgroups   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 $\pi_1(M)=\Gamma$ where $\Gamma$ is a lattice in $G=SO(n,1)$. The
theorem can be rephrased in the following format. Let $X(\Z,\Gamma)$ be the
space of representations of $\Z$ into $\Gamma$ modulo conjugation by $\Gamma$.
$X(\Z,G)$ is defined similarly. Let $\pi: X(\Z,\Gamma)\to X(\Z,G)$ be the
projection map. The PGT provides a volume form $vol$ on $X(\Z,G)$ such that for
sequences of subsets $\{B_t\}$, $B_t \subset X(\Z,G)$ satisfying certain
explicit hypotheses, $|\pi^{-1}(B_t)|$ is asymptotic to $vol(B_t)$.
  We prove a statement having a similar format in which $\Z$ is replaced by a
free group of finite rank under the additional hypothesis that $n=2$ or 3.

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The categories of this paper are: hep-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: cs
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The categories of this paper are: hep-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: astro-ph
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The categories of this paper are: solv-int
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The categories of this paper are: nlin
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The categories of this paper are: mtrl-th
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The categories of this paper are: cond-mat
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The categories of this paper are: acc-phys
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The categories of this paper are: plasm-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-lat
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The categories of this paper are: quant-ph