Left-Garside categories, self-distributivity, and braids
Group Theory
2008-10-28 v1
Abstract
In connection with the emerging theory of Garside categories, we develop the notions of a left-Garside category and of a locally left-Garside monoid. In this framework, the connection between the self-distributivity law LD and braids amounts to the result that a certain category associated with LD is a left-Garside category, which projects onto the standard Garside category of braids. This approach leads to a realistic program for establishing the Embedding Conjecture of [Dehornoy, Braids and Self-distributivity, Birkhauser (2000), Chap. IX].
Keywords
Cite
@article{arxiv.0810.4698,
title = {Left-Garside categories, self-distributivity, and braids},
author = {Patrick Dehornoy},
journal= {arXiv preprint arXiv:0810.4698},
year = {2008}
}