Braidoids are defined and shown to satisfy analogues of the Alexander and Markov theorems, so planar knotoids can be braided and braidoid equivalence corresponds to knotoid isotopy.
The virtual and universal braids, Fundamenta Mathematicae 184 (2004) 159–186
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Braidoids
Braidoids are defined and shown to satisfy analogues of the Alexander and Markov theorems, so planar knotoids can be braided and braidoid equivalence corresponds to knotoid isotopy.