Knotoids, Braidoids and Applications

This paper is an introduction to the theory of braidoids. Braidoids are geometric objects analogous to classical braids, forming a counterpart theory to the theory of knotoids. We introduce these objects and their topological equivalences, and we conclude with a potential application to the study of proteins.

[1]  S. Lambropoulou.  Braid equivalences and the L-moves , 2011, 1103.4397.

[2]  E. Artin.  The theory of braids. , 1950, American scientist.

[3]  L. Kauffman,et al.  Virtual Braids , 2004, math/0407349.

[4]  H. Morton.  Threading knot diagrams , 1986, Mathematical Proceedings of the Cambridge Philosophical Society.

[5]  Vaughan F. R. Jones,et al.  Hecke algebra representations of braid groups and link polynomials , 1987 .

[6]  Louis H. Kauffman,et al.  New invariants of knotoids , 2016, Eur. J. Comb..

[7]  M. Ziegler.  Volume 152 of Graduate Texts in Mathematics , 1995 .

[8]  K. Reidemeister.  Elementare Begründung der Knotentheorie , 1927 .

[9]  J. Birman.  Braids, Links, and Mapping Class Groups. , 1975 .

[10]  C. Rourke,et al.  Markov's theorem in 3-manifolds , 1997, math/0405498.

[11]  S. Lambropoulou.  A study of braids in 3-manifolds , 1993 .

[12]  Pierre Vogel,et al.  Representation of links by braids: A new algorithm , 1990 .

[13]  Emil Artin,et al.  Theorie der Zöpfe , 1925 .

[14]  Hiroki Morizono,et al.  Structures of N‐acetylornithine transcarbamoylase from Xanthomonas campestris complexed with substrates and substrate analogs imply mechanisms for substrate binding and catalysis , 2006, Proteins.

[15]  J W Alexander,et al.  A Lemma on Systems of Knotted Curves. , 1923, Proceedings of the National Academy of Sciences of the United States of America.

[16]  Julien Dorier,et al.  Studies of global and local entanglements of individual protein chains using the concept of knotoids , 2017, Scientific Reports.

[17]  Vaughan F. R. Jones.  Index for subfactors , 1983 .

[18]  Shuji Yamada.  The minimal number of Seifert circles equals the braid index of a link , 1987 .

[19]  Julien Dorier,et al.  Topological Models for Open-Knotted Protein Chains Using the Concepts of Knotoids and Bonded Knotoids , 2017, Polymers.

[20]  K Schulten,et al.  VMD: visual molecular dynamics. , 1996, Journal of molecular graphics.

[21]  T. N. Bhat,et al.  The Protein Data Bank , 2000, Nucleic Acids Res..