Results 1 to 10 of about 6,624,762 (188)
Symmetry, 2012 This paper is a very brief introduction to knot theory. It describes knot coloring by quandles, the fundamental group of a knot complement, and handle-decompositions of knot complements.
J Scott Carter
exaly +4 more sources
Knot theory in modern chemistry [PDF]
Chemical Society Reviews, 2016 This tutorial review provides an introduction to the mathematics of knots and topological concepts in the context of the chemical sciences.
Kate E Horner
exaly +5 more sources
Knot theory and error-correcting codes. [PDF]
Des Codes CryptogrAbstract This paper builds a novel bridge between algebraic coding theory and mathematical knot theory, with applications in both directions. We give methods to construct error-correcting codes starting from the colorings of a knot, describing through a series of results how the properties of the knot translate into code parameters.
Kılıç AB +3 more
europepmc +8 more sources
Knot theory realizations in nematic colloids. [PDF]
Proc Natl Acad Sci U S A, 2015 Čopar S +3 more
europepmc +3 more sources
European Journal of Combinatorics, 1999 Virtual knot theory is a generalization (discovered by the author in 1996) of knot theory to the study of all oriented Gauss codes. (Classical knot theory is a study of planar Gauss codes.) Graph theory studies non-planar graphs via graphical diagrams with virtual crossings.
L. Kauffman
openaire +4 more sources
Unsolved problems in virtual knot theory and combinatorial knot theory [PDF]
Banach Center Publications, 2014 65 pages, 24 figures.
Fenn, Roger +3 more
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Circuit complexity of knot states in Chern-Simons theory [PDF]
Journal of High Energy Physics, 2019 We compute an upper bound on the circuit complexity of quantum states in 3d Chern-Simons theory corresponding to certain classes of knots. Specifically, we deal with states in the torus Hilbert space of Chern-Simons that are the knot complements on the 3-
Giancarlo Camilo +3 more
doaj +2 more sources
Knot data analysis using multiscale Gauss link integral. [PDF]
Proc Natl Acad Sci U S A, 2023 Significance Knot theory is a pivotal mathematical branch and has garnered tremendous research interest for over 200 years. Despite its broad applications, it has been limited to qualitative analysis.
Shen L +5 more
europepmc +2 more sources
INTRODUCTION TO VIRTUAL KNOT THEORY [PDF]
Journal of Knot Theory and Its Ramifications, 2011 This paper is an introduction to virtual knot theory and an exposition of new ideas and constructions, including the parity bracket polynomial, the arrow polynomial, the parity arrow polynomial and categorifications of the arrow polynomial.
L. Kauffman
openaire +6 more sources
Deep learning the hyperbolic volume of a knot
Physics Letters B, 2019 An important conjecture in knot theory relates the large-N, double scaling limit of the colored Jones polynomial JK,N(q) of a knot K to the hyperbolic volume of the knot complement, Vol(K).
Vishnu Jejjala +2 more
doaj +3 more sources