A USER’S GUIDE TO THE MAPPING CLASS

GROUP: ONCE PUNCTURED SURFACES

Lee Mosher

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.

Typeset by AMS-TEX