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In this paper we discuss algebraic, combinatorial and topological propertiesof singular virtual braids. On the algebraic side we state the relationsbetween classical and virtual singular objects, in addition we discuss aBirman-like conjecture for the virtual case. On the topological andcombinatorial side, we prove that there is a bijection between singularabstract braids, horizontal Gauss diagrams and singular virtual braids, inparticular using horizontal Gauss diagrams we obtain a presentation of thesingular pure virtual braid monoid.

Algebraic, combinatorial and topological properties of singular virtual braid monoids