The Fundamental Group of $SO(n)$ Via Quotients of Braid Groups
History and Overview
2016-07-21 v1 Group Theory
Geometric Topology
Abstract
We describe an algebraic proof of the well-known topological fact that . The fundamental group of appears in our approach as the center of a certain finite group defined by generators and relations. The latter is a factor group of the braid group , obtained by imposing one additional relation and turns out to be a nontrivial central extension by of the corresponding group of rotational symmetries of the hyperoctahedron in dimension .
Cite
@article{arxiv.1607.05876,
title = {The Fundamental Group of $SO(n)$ Via Quotients of Braid Groups},
author = {Ina Hajdini and Orlin Stoytchev},
journal= {arXiv preprint arXiv:1607.05876},
year = {2016}
}