The 6-strand braid group is CAT(0)
Group Theory
2016-09-01 v2 Combinatorics
Abstract
We show that braid groups with at most 6 strands are CAT(0) using the close connection between these groups, the associated non-crossing partition complexes and the embeddability of their diagonal links into spherical buildings of type A. Furthermore, we prove that the orthoscheme complex of any bounded graded modular complemented lattice is CAT(0), giving a partial answer to a conjecture of Brady and McCammond.
Keywords
Cite
@article{arxiv.1304.5990,
title = {The 6-strand braid group is CAT(0)},
author = {Thomas Haettel and Dawid Kielak and Petra Schwer},
journal= {arXiv preprint arXiv:1304.5990},
year = {2016}
}
Comments
27 pages, 13 figures. To appear in Geometriae Dedicata, the final publication is available at Springer via http://dx.doi.org/10.1007/s10711-015-0138-9