Groupoid-theoretical methods in the mapping class groups of surfaces

Details Groupoid-theoretical methods in the mapping class groups of surfaces Groupoid-theoretical methods in the mapping class groups of surfaces

2011-09-29

arxiv.org/abs/1109.6479v2

Mathematics

Geometric Topology

41 pages, 7 figures

Scientific paper

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 in the case the boundary is connected.

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