Abstract
Given a biquandle [Formula: see text], a function [Formula: see text] with certain compatibility and a pair of non commutative cocyles [Formula: see text] with values in a non necessarily commutative group [Formula: see text], we give an invariant for singular knots/links. Given [Formula: see text], we also define a universal group [Formula: see text] and universal functions governing all 2-cocycles in [Formula: see text], and exhibit examples of computations. When the target group is abelian, a notion of abelian cocycle pair is given and the “state sum” is defined for singular knots/links. Computations generalizing linking number for singular knots are given. As for virtual knots, a “self-linking number” may be defined for singular knots.
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