Groupoid-theoretical methods in the mapping class groups of surfaces

Nariya Kawazumi; Yusuke Kuno

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arXiv · 1109.6479

Groupoid-theoretical methods in the mapping class groups of surfaces

Nariya Kawazumi·Yusuke Kuno

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Abstract

We provide some language for algebraic study of the mapping class groups for surfaces with non-connected boundary. As applications, we generalize our previous results on Dehn twists to any compact connected oriented surfaces with non-empty boundary. Moreover we embed the `smallest' Torelli group in the sense of Putman into a pro-nilpotent group coming from the Goldman Lie algebra. The graded quotients of the embedding equal the Johnson homomorphisms of all degrees if the boundary is connected.

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Nariya Kawazumi, Yusuke Kuno. 2012-10-21. Groupoid-theoretical methods in the mapping class groups of surfaces. https://arxiv.org/abs/1109.6479

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