On word reversing in braid groups

Details On word reversing in braid groups On word reversing in braid groups

2004-07-20

arxiv.org/abs/math/0407333v1

Mathematics

Group Theory

Scientific paper

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.

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