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

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

1994-09-09

arxiv.org/abs/math/9409209v1

Geometric and computational perspectives on infinite groups, 101--174, DIMACS Ser. Discrete Math. Theoret. Comput. Sci. 25, Am

Mathematics

Geometric Topology

Scientific paper

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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