ALGEBRAIC, COMBINATORIAL AND TOPOLOGICAL PROPERTIES OF SINGULAR VIRTUAL BRAID MONOIDS

Bruno Aarón , Cisneros De , L A Cruz , Bruno Aaron Cisneros de La Cruz (1) , Guillaume Gandolfi (2)

1 UNAM - Universidad Nacional Autónoma de México = National Autonomous University of Mexico
2 LMNO - Laboratoire de Mathématiques Nicolas Oresme

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.

Domaines: Topologie géométrique [math.GT]; Théorie des groupes [math.GR]

Bruno Aarón, Cisneros De, L A Cruz, Bruno Aaron Cisneros de La Cruz, Guillaume Gandolfi. ALGEBRAIC, COMBINATORIAL AND TOPOLOGICAL PROPERTIES OF SINGULAR VIRTUAL BRAID MONOIDS. Journal of Knot Theory and Its Ramifications, In press, 28 (10), pp.1950069. ⟨10.1142/S021821651950069X⟩. ⟨hal-02321864⟩