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A Survey on Knotoids, Braidoids and Their Applications

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Knots, Low-Dimensional Topology and Applications (KNOTS16 2016)

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Abstract

This paper is a survey on the theory of knotoids and braidoids. Knotoids are open ended knot diagrams in surfaces and braidoids are geometric objects analogous to classical braids, forming a counterpart theory to the theory of knotoids in the plane. We survey through the fundamental notions and existing works on these objects as well as their applications in the study of proteins.

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Acknowledgements

The research of Sofia Lambropoulou and Neslihan Gügümcü has been co-financed by the European Union (European Social Fund - ESF) and Greek national funds through the Operational Program IJEducation and Lifelong Learning of the National Strategic Reference Framework (NSRF) - Research Funding Program: THALES: Reinforcement of the interdisciplinary and/or inter-institutional research and innovation, MIS: 380154. Louis H. Kauffman’ s work was supported by the Laboratory of Topology and Dynamics, Novosi- birsk State University (contract no. 14.Y26.31.0025 with the Ministry of Education and Science of the Russian Federation)

Author information

Authors and Affiliations

  1. School of Applied Mathematical and Physical Sciences, National Technical University of Athens, Zografou Campus, 157 80, Athens, Greece

    Neslihan Gügümcü & Sofia Lambropoulou

  2. Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, 851 South Morgan St., Chicago, IL, 60607-7045, USA

    Louis H. Kauffman

  3. Department of Mechanics and Mathematics, Novosibirsk State University, Novosibirsk, Russia

    Louis H. Kauffman

Authors
  1. Neslihan Gügümcü
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  2. Louis H. Kauffman
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  3. Sofia Lambropoulou
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Corresponding author

Correspondence to Neslihan Gügümcü .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Williams College, Williamstown, MA, USA

    Colin C. Adams

  2. Department of Mathematics, University of Texas at Austin, Austin, TX, USA

    Cameron McA. Gordon

  3. Department of Mathematics, Vanderbilt University, Nashville, TN, USA

    Vaughan F.R. Jones

  4. Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, Chicago, IL, USA

    Louis H. Kauffman

  5. School of Applied Mathematical and Physical Sciences, National Technical University of Athens, Athens, Greece

    Sofia Lambropoulou

  6. Department of Mathematics, University of California, Santa Barbara, Santa Barbara, CA, USA

    Kenneth C. Millett

  7. Department of Mathematics, Columbian College of Arts & Sciences, George Washington University, Washington, DC, USA

    Jozef H. Przytycki

  8. Department of Mathematics and Applications, University of Milano-Bicocca, Milano, Italy

    Renzo Ricca

  9. Department of Mathematics, North Carolina State University, Raleigh, NC, USA

    Radmila Sazdanovic

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Gügümcü, N., Kauffman, L.H., Lambropoulou, S. (2019). A Survey on Knotoids, Braidoids and Their Applications. In: Adams, C., et al. Knots, Low-Dimensional Topology and Applications. KNOTS16 2016. Springer Proceedings in Mathematics & Statistics, vol 284. Springer, Cham. https://doi.org/10.1007/978-3-030-16031-9_19

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