Affiliation:
1. Department of Mathematical Sciences, KAIST, Daehak-ro Yuseong-gu, Daejeon, South Korea
Abstract
Abstract
In this paper, we show that the minimal asymptotic translation length of the Torelli group ${\mathcal{I}}_g$ of the surface $S_g$ of genus $g$ on the curve graph asymptotically behaves like $1/g$, contrary to the mapping class group ${\textrm{Mod}}(S_g)$, which behaves like $1/g^2$. We also show that the minimal asymptotic translation length of the pure braid group ${\textrm{PB}}_n$ on the curve graph asymptotically behaves like $1/n$, contrary to the braid group ${\textrm{B}}_n$, which behaves like $1/n^2$.
Funder
Samsung Science & Technology Foundation
National Research Foundation of Korea
Publisher
Oxford University Press (OUP)
Cited by
3 articles.
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