A lower bound of the distortion of the Torelli group in the mapping class group with boundary components

Erika Kuno; Genki Omori

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arXiv · 1609.06811

A lower bound of the distortion of the Torelli group in the mapping class group with boundary components

Erika Kuno·Genki Omori

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Abstract

We prove that each Torelli group of an orientable surface with any number of boundary components is at least exponentially distorted in the mapping class group by using Broaddus-Farb-Putman's techniques. Further we show that the distortion of each Torelli group in the level $d$ mapping class group is the same as that of in the mapping class group.

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Erika Kuno, Genki Omori. 2016-09-22. A lower bound of the distortion of the Torelli group in the mapping class group with boundary components. https://arxiv.org/abs/1609.06811

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