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Braidoids

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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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Article 20 July 2021

Diego Arcis & Jesús Juyumaya

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Acknowledgement

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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Authors and Affiliations

  1. Department of Mathematics, Izmir Institute of Technology, Gülbahçe Mah., URLA, 35430, İzmir, Turkey

    Neslihan Gügümcü

  2. School of Applied Mathematical and Physical Sciences, National Technical University of Athens, Zografou Campus, GR-15780, Athens, Greece

    Sofia Lambropoulou

Authors
  1. Neslihan Gügümcü
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  2. Sofia Lambropoulou
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Correspondence to Neslihan Gügümcü.

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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

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