Counting closed geodesics in Moduli space

@inproceedings{Eskin2008CountingCG,
  title={Counting closed geodesics in Moduli space},
  author={Alex Eskin and Maryam Mirzakhani},
  year={2008}
}
Let Mg denote the moduli space of Riemann surfaces of genus g. We may write Mg = Tg/Γ, where Tg is the Teichmüller space of genus g surfaces, and Γ is the mapping class group. Let N(R) denote the number of closed geodesics in Mg of length at most R. Then N(R) is also the number of conjugacy classes of pseudo-anosov elements of the mapping class group of translation length at most R. Our main result is the following: