New York Journal of Mathematics
Volume 20 (2014) 989-999


Aaron D. Valdivia

Asymptotic translation length in the curve complex

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Published: October 31, 2014
Keywords: Curve complex; translation length; asymptotic; pseudo-Anosov; mapping class group
Subject: 30F60, 32G15

We prove the minimal pseudo-Anosov translation length in the curve complex behaves like (1/ϗ(Sg,n)2) for sequences where g=rn for some r∈Q. We also show that if the genus is fixed as n→ ∞ then the behavior is (1/|ϗ(Sg,n)|). This extends results of Gadre and Tsai and answers a conjecture of theirs in the affirmative.

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