A User's Guide to the Mapping Class Group: Once Punctured Surfaces
Geometric Topology
2016-09-06 v1
Abstract
This document is a practical guide to computations using an automatic structure for the mapping class group of a once-punctured, oriented surface . We describe a quadratic time algorithm for the word problem in this group, which can be implemented efficiently with pencil and paper. The input of the algorithm is a word, consisting of ``chord diagrams'' of ideal triangulations and elementary moves, which represents an element of the mapping class group. The output is a word called a ``normal form'' that uniquely represents the same group element.
Cite
@article{arxiv.math/9409209,
title = {A User's Guide to the Mapping Class Group: Once Punctured Surfaces},
author = {Lee Mosher},
journal= {arXiv preprint arXiv:math/9409209},
year = {2016}
}