Plat closures of spherical braids in $\mathbb{R}P^3$
Geometric Topology
2023-11-15 v3
Abstract
We define plat closure for spherical braids to obtain links in and prove that all links in can be realized in this manner. Given a spherical braid of strands in we associate a permutation on elements called \textit{residual permutation}. We prove that the number of components of the plat closure link of a spherical braid is same as the number of disjoint cycles in . We also present a set of moves on spherical braids in the same spirit as the classical Markov moves on braids. The completeness of this set of moves to capture the entire isotopy classes of the plat closure links is still to be explored.
Keywords
Cite
@article{arxiv.2304.08954,
title = {Plat closures of spherical braids in $\mathbb{R}P^3$},
author = {Rama Mishra and Visakh Narayanan},
journal= {arXiv preprint arXiv:2304.08954},
year = {2023}
}
Comments
20 Pages, 22 Figures, preliminary version