Growth Rate Of Dehn Twist Lattice Points In Teichm\"{u}ller Space

Athreya, Bufetov, Eskin and Mirzakhani [2] have shown the number of mapping class group lattice points intersecting a closed ball of radius R in Teichmüller space is asymptotic to e, where h is the dimension of the Teichmüller space. In contrast we show the number of Dehn twist lattice points intersecting a closed ball of radius R is coarsely asymptotic to e h 2 . Moreover, we show the number multi-twist lattice points intersecting a closed ball of radius R grows coarsely at least at the rate of R · e h 2 .

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