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Paper detail

Groupoid-theoretical methods in the mapping class groups of surfaces

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.

preprint2012arXivOpen access
Nariya KawazumiYusuke Kuno
math.GT
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Nariya KawazumiYusuke Kuno

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