Abstract
Athreya et al. [Lattice point asymptotics and volume growth on Teichmüller space, Duke Math. J. 161 (2012) 1055–1111] have shown the number of mapping class group lattice points intersecting a closed ball of radius [Formula: see text] in Teichmüller space is asymptotic to [Formula: see text], where [Formula: see text] is the dimension of the Teichmüller space. In contrast we show the number of Dehn twist lattice points intersecting a closed ball of radius [Formula: see text] is coarsely asymptotic to [Formula: see text]. Moreover, we show the number multi-twist lattice points intersecting a closed ball of radius [Formula: see text] grows coarsely at least at the rate of [Formula: see text].
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