On word reversing in braid groups
Group Theory
2007-05-23 v1
Abstract
It has been conjectured that in a braid group, or more generally in a Garside group, applying any sequence of monotone equivalences and word reversings can increase the length of a word by at most a linear factor depending on the group presentation only. We give a counter-example to this conjecture, but, on the other hand, we establish length upper bounds for the case when only right reversing is involved. We also state a new conjecture which would, like the above one, imply that the space complexity of the handle reduction algorithm is linear.
Cite
@article{arxiv.math/0407333,
title = {On word reversing in braid groups},
author = {Patrick Dehornoy and Bert Wiest},
journal= {arXiv preprint arXiv:math/0407333},
year = {2007}
}