Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Counting Conjugacy Classes in $Out(F_N)$   We show that if a f.g. group $G$ has a non-elementary WPD action on a
hyperbolic metric space $X$, then the number of $G$-conjugacy classes of
$X$-loxodromic elements of $G$ coming from a ball of radius $R$ in the Cayley
graph of $G$ grows exponentially in $R$. As an application we prove that for
$N\ge 3$ the number of distinct $Out(F_N)$-conjugacy classes of fully
irreducibles $\phi$ from an $R$-ball in the Cayley graph of $Out(F_N)$ with
$\log\lambda(\phi)$ on the order of $R$ grows exponentially in $R$.

34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
14
The categories of this paper are: math-ph
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol