2019/04/01 by Bruno Aarón Cisneros de la Cruz, de la Cruz, Bruno Aaron Cisneros, Guillaume Gandolfi +1
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.1904.00951
openalex publication_date 2019/04/01 · openalex created_date 2022/07/29 · openalex updated_date 2026/07/28
In this paper we discuss algebraic, combinatorial and topological properties\nof singular virtual braids. On the algebraic side we state the relations\nbetween classical and virtual singular objects, in addition we discuss a\nBirman-like conjecture for the virtual case. On the topological and\ncombinatorial side, we prove that there is a bijection between singular\nabstract braids, horizontal Gauss diagrams and singular virtual braids, in\nparticular using horizontal Gauss diagrams we obtain a presentation of the\nsingular pure virtual braid monoid.\n