Minimal asymptotic translation lengths of Torelli groups and pure braid groups on the curve graph

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In this paper, we show that the minimal asymptotic translation length of the Torelli group 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 Mod(S-g), which behaves like 1/g(2). We also show that the minimal asymptotic translation length of the pure braid group PBn on the curve graph asymptotically behaves like 1/n, contrary to the braid group B-n, which behaves like 1/n(2).
Publisher
OXFORD UNIV PRESS
Issue Date
2020-12
Language
English
Article Type
Article
Citation

INTERNATIONAL MATHEMATICS RESEARCH NOTICES, v.2020, no.24, pp.9974 - 9987

ISSN
1073-7928
DOI
10.1093/imrn/rny273
URI
http://hdl.handle.net/10203/280075
Appears in Collection
MA-Journal Papers(저널논문)
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