On Complexity of the Word Problem in Braid Groups and Mapping Class Groups
几何拓扑
2016-09-07 v1
摘要
We prove that the word problem in the mapping class group of the once-punctured surface of genus g has complexity O(|w|^2 g for |w| > log(g) where |w| is the length of the word in a (standard) set of generators. The corresponding bound in the case of the closed surface is O(|w|^2 g^2). We also carry out the same methods for the braid groups, and show that this gives a bound which improves the best known bound in this case; namely, the complexity of the word problem in the n-braid group is O(|w|^2 n), for |w| > log n. We state a similar result for mapping class groups of surfaces with several punctures.
引用
@article{arxiv.math/9809154,
title = {On Complexity of the Word Problem in Braid Groups and Mapping Class Groups},
author = {Hessam Hamidi-Tehrani},
journal= {arXiv preprint arXiv:math/9809154},
year = {2016}
}
备注
29 pages, 12 figures. To appear in Topology and its applications