Algebraic, combinatorial and topological properties of singular virtual braid monoids
Geometric Topology
2019-04-03 v2 Group Theory
Abstract
In this paper we discuss algebraic, combinatorial and topological properties of singular virtual braids. On the algebraic side we state the relations between classical and virtual singular objects, in addition we discuss a Birman-like conjecture for the virtual case. On the topological and combinatorial side, we prove that there is a bijection between singular abstract braids, horizontal Gauss diagrams and singular virtual braids, in particular using horizontal Gauss diagrams we obtain a presentation of the singular pure virtual braid monoid.
Keywords
Cite
@article{arxiv.1904.00951,
title = {Algebraic, combinatorial and topological properties of singular virtual braid monoids},
author = {Bruno Aaron Cisneros de la Cruz and Guillaume Gandolfi},
journal= {arXiv preprint arXiv:1904.00951},
year = {2019}
}
Comments
17 pages, 13 figures