On Complexity of the Word Problem in Braid Groups and Mapping Class Groups

Details On Complexity of the Word Problem in Braid Groups and Mapping Class Groups On Complexity of the Word Problem in Braid Groups and Mapping Class Groups

1998-09-28

arxiv.org/abs/math/9809154v1

Mathematics

Geometric Topology

29 pages, 12 figures. To appear in Topology and its applications

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

On Complexity of the Word Problem in Braid Groups and Mapping Class Groups does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On Complexity of the Word Problem in Braid Groups and Mapping Class Groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On Complexity of the Word Problem in Braid Groups and Mapping Class Groups will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-482125