The Relaxation Normal Form of Braids is Regular
Combinatorics
2017-10-13 v4 Geometric Topology
Abstract
Braids can be represented geometrically as laminations of punctured disks. The geometric complexity of a braid is the minimal complexity of a lamination that represents it, and tight laminations are representatives of minimal complexity. These laminations give rise to a normal form of braids, via a relaxation algorithm. We study here this relaxation algorithm and the associated normal form. We prove that this normal form is regular and prefix-closed. We provide an effective construction of a deterministic automaton that recognizes this normal form.
Keywords
Cite
@article{arxiv.1507.03248,
title = {The Relaxation Normal Form of Braids is Regular},
author = {Vincent Jugé},
journal= {arXiv preprint arXiv:1507.03248},
year = {2017}
}
Comments
38 pages, 27 figures