Growth of pseudo-Anosov conjugacy classes in Teichmüller space

[摘要] Athreya, Bufetov, Eskin and Mirzakhani (2012) have shown that the number of mapping class group lattice points intersecting a closed ball of radius RRR in Teichmüller space is asymptotic to ehRe^{hR}ehR, where hhh is the dimension of the Teichmüller space. We show for any pseudo-Anosov mapping class fff, there exists a power nnn, such that the number of lattice points of the fnf^nfn conjugacy class intersecting a closed ball of radius RRR is coarsely asymptotic to eh2Re^{\frac{h}{2}R}e2h​R.

[学科分类] 神经科学

[关键词] Teichmüller theory;mapping class groups