Year: 2009
Type: preprint
Abstract: We show that for any given n, there exists a sequence of words a_k in the generators sigma_1, ... sigma_{n-1} of the braid group B_n, representing the identity element of B_n, such that the number of braid relations of the form sigma_i sigma_{i+1} sigma_i = sigma_{i+1} sigma_i sigma_{i+1} needed to pass from a_k to the empty word is quadratic with respect to the length of a_k.
Source: arXiv (Cornell University)
Authors: Hass, Joel, Kalka, Arkadius, Nowik, Tahl
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1502736099