Results 11 to 20 of about 34,079 (89)
Untangling the Mechanics and Topology in the Frictional Response of Long Overhand Elastic Knots [PDF]
, 2015 We combine experiments and theory to study the mechanics of overhand knots in slender elastic rods under tension. The equilibrium shape of the knot is governed by an interplay between topology, friction, and bending. We use precision model experiments to
Audoly, B. +3 more
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Chirality of Knots $9_{42}$ and $10_{71}$ and Chern-Simons Theory [PDF]
, 1994 Upto ten crossing number, there are two knots, $9_{42}$ and $10_{71}$ whose chirality is not detected by any of the known polynomials, namely, Jones invariants and their two variable generalisations, HOMFLY and Kauffman invariants.
Govindarajan, T. R. +2 more
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The forbidden number of a knot [PDF]
, 2014 Every classical or virtual knot is equivalent to the unknot via a sequence of extended Reidemeister moves and the so-called forbidden moves. The minimum number of forbidden moves necessary to unknot a given knot is an invariant we call the {\it forbidden
Crans, Alissa +2 more
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A Self-Linking Invariant of Virtual Knots [PDF]
, 2004 In this paper we introduce a new invariant of virtual knots and links that is non-trivial for infinitely many virtuals, but is trivial on classical knots and links.
Kauffman, Louis H.
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Legendrian and transverse twist knots
, 2011 In 1997, Chekanov gave the first example of a Legendrian nonsimple knot type: the $m(5_2)$ knot. Epstein, Fuchs, and Meyer extended his result by showing that there are at least $n$ different Legendrian representatives with maximal Thurston--Bennequin ...
Etnyre, John B. +2 more
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, 2012 Classical knots in $\mathbb{R}^3$ can be represented by diagrams in the plane. These diagrams are formed by curves with a finite number of transverse crossings, where each crossing is decorated to indicate which strand of the knot passes over at that ...
Henrich, Allison +5 more
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Virtual Knot Theory --Unsolved Problems
, 2005 This paper is an introduction to the theory of virtual knots and links and it gives a list of unsolved problems in this subject.Comment: 33 pages, 7 figures, LaTeX ...
Fenn, Roger +2 more
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Knot Probabilities in Random Diagrams
, 2015 We consider a natural model of random knotting- choose a knot diagram at random from the finite set of diagrams with n crossings. We tabulate diagrams with 10 and fewer crossings and classify the diagrams by knot type, allowing us to compute exact ...
Cantarella, Jason +2 more
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Post Quantum Cryptography from Mutant Prime Knots
, 2010 By resorting to basic features of topological knot theory we propose a (classical) cryptographic protocol based on the `difficulty' of decomposing complex knots generated as connected sums of prime knots and their mutants.
Adams C. +13 more
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Bridge numbers for virtual and welded knots
, 2014 Using Gauss diagrams, one can define the virtual bridge number ${\rm vb}(K)$ and the welded bridge number ${\rm wb}(K),$ invariants of virtual and welded knots with ${\rm wb}(K) \leq {\rm vb}(K).$ If $K$ is a classical knot, Chernov and Manturov showed ...
Boden, Hans U., Gaudreau, Anne Isabel
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