Groupoid-theoretical methods in the mapping class groups of surfaces
Geometric Topology
2012-10-23 v3
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.
Cite
@article{arxiv.1109.6479,
title = {Groupoid-theoretical methods in the mapping class groups of surfaces},
author = {Nariya Kawazumi and Yusuke Kuno},
journal= {arXiv preprint arXiv:1109.6479},
year = {2012}
}
Comments
43 pages, 7 figures