Abstract
Braidoids generalize the classical braids and form a counterpart theory to the theory of planar knotoids, just as the theory of braids does for the theory of knots. In this paper, we introduce basic notions of braidoids, a closure operation for braidoids, we prove an analogue of the Alexander theorem, that is, an algorithm that turns a knotoid into a braidoid, and we formulate and prove a geometric analogue of the Markov theorem for braidoids using the L-moves.
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The first author cordially thanks the Oberwolfach Research Institute for Mathematics for providing her a peaceful research environment whilst completing this paper.
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Gügümcü, N., Lambropoulou, S. Braidoids. Isr. J. Math. 242, 955–995 (2021). https://doi.org/10.1007/s11856-021-2155-8
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DOI: https://doi.org/10.1007/s11856-021-2155-8