A User's Guide to the Mapping Class Group: Once Punctured Surfaces

Lee Mosher

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A User's Guide to the Mapping Class Group: Once Punctured Surfaces

Lee Mosher

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Abstract

This document is a practical guide to computations using an automatic structure for the mapping class group of a once-punctured, oriented surface $S$. 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.

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Lee Mosher. 1994-09-09. A User's Guide to the Mapping Class Group: Once Punctured Surfaces. https://arxiv.org/abs/math/9409209

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