Groupoids and the algebra of rewriting in group presentations
Group Theory
2019-01-15 v1
Abstract
Presentations of groups by rewriting systems (that is, by monoid presentations), have been fruitfully studied by encoding the rewriting system in a --complex -- the Squier complex -- whose fundamental groupoid then describes the derivation of consequences of the rewrite rules. We describe a reduced form of the Squier complex, investigate the structure of its fundamental groupoid, and show that key properties of the presentation are still encoded in the reduced form.
Keywords
Cite
@article{arxiv.1901.04348,
title = {Groupoids and the algebra of rewriting in group presentations},
author = {N. D. Gilbert and E. A. McDougall},
journal= {arXiv preprint arXiv:1901.04348},
year = {2019}
}
Comments
15 pages