On isotopy classes of three dimmensional knots and their invariants

Călugăreanu, Grigore

doi:10.21136/cmj.1961.100486

Cited by 236 publications

(53 citation statements)

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“…In order to further understand the meaning of this term, we discuss the fact that, independently, Calugareanu [10] defined a real-valued invariant of a smooth simple closed curve in 3 ℜ by allowing the two curves in Gauss's linking integral to come together. In the limit, points ( ) x s and ( )…”

Section: The Biot-savart Formula and Helicitymentioning

confidence: 99%

A Self-Linking Field Formalism

Klingman¹

2021

JMP

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The Gauss-linking integral for disjoint oriented smooth closed curves is derived linking integrals from the Biot-Savart description of the magnetic field. DeTurck and Gluck extend this linking from 3-space 3 R to () 2 SU space of the unit 3-sphere and hyperbolic space in Minkowski 1,3 R. I herein extend Gauss-linking to self-linking and develop the concept of self-dual, which is then applied to gravitomagnetic dynamics. My purpose is to redefine Wheeler's geon from unstable field structures based on the electromagnetic field to self-stabilized gravitomagnetic field structures.

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Section: The Biot-savart Formula and Helicitymentioning

confidence: 99%

A Self-Linking Field Formalism

Klingman¹

2021

JMP

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“…4. Now, recall the Călugăreanu-White theorem [48][49][50], which relates and defines the linking number G, the writhe W, and the twist T of two curves as [23,47]…”

Section: Wilson Fermions In Three-dimensional Euclidean Spacetimementioning

confidence: 99%

“…(53), we see that for θ ¼ π and after rescaling b jμ → b jμ =ð2πÞ, the latter is the same as the one arising in the partition function [Eq. (49)] up to the sign of the CS term. As far as the partition function is concerned, the sign of the CS term is immaterial, since integrating out either a jμ or b jμ in the J → ∞ limit leads to the same vortex current interaction when θ ¼ π as we sum over all integer-valued vortex currents.…”

Section: A Particle-vortex Duality On the Latticementioning

confidence: 99%

Bosonization in 2+1 dimensions via Chern-Simons bosonic particle-vortex duality

et al. 2020

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Dualities provide deep insight into physics by relating two seemingly distinct theories. Here we consider a duality between lattice fermions and bosons in (2 þ 1) spacetime dimensions, relating free massive Dirac fermions to Abelian Chern-Simons Higgs (ACSH) bosons. To establish the duality, we represent the exact partition function of the lattice fermions in terms of the writhe of fermionic worldlines. On the bosonic side, the partition function is expressed in the writhe of the vortex loops of the particle-vortex dual of the ACSH Lagrangian. In the continuum and scaling limit, we show these to be identical. This result can be understood from the closed fermionic worldlines being direct mappings of the ACSH vortex loops, with the writhe keeping track of particle statistics.

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“…where DTw is the deviation of DNA twist from its value in the torsionally relaxed DNA and Wr is a measure of chirality of DNA conformation (20,31). The value of DLk does not change during conformational changes in the circular DNA at particular solution conditions, whereas the partitioning between DTw and Wr is different, in general, for each DNA conformation.…”

Section: Conformational Properties Of Supercoiled Torus Catenanesmentioning

confidence: 99%

Unlinking of Supercoiled DNA Catenanes by Type IIA Topoisomerases

Vologodskii

2011

Biophysical Journal

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It was found recently that DNA catenanes, formed during replication of circular plasmids, become positively (+) supercoiled, and the unlinking of such catenanes by type IIA topoisomerases proceeds much more efficiently than the unlinking of negatively (-) supercoiled catenanes. In an attempt to explain this striking finding we studied, by computer simulation, conformational properties of supercoiled DNA catenanes. Although the simulation showed that conformational properties of (+) and (-) supercoiled replication catenanes are very different, these properties per se do not give any advantage to (+) supercoiled over (-) supercoiled DNA catenanes for unlinking. An advantage became evident, however, when we took into account the established features of the enzymatic reaction catalyzed by the topoisomerases. The enzymes create a sharp DNA bend in the first bound DNA segment and allow for the transport of the second segment only from inside the bend to its outside. We showed that in (-) supercoiled DNA catenanes this protein-bound bent segment becomes nearly inaccessible for segments of the other linked DNA molecule, inhibiting the unlinking.

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On isotopy classes of three dimmensional knots and their invariants

Cited by 236 publications

References 0 publications

A Self-Linking Field Formalism

A Self-Linking Field Formalism

Bosonization in 2+1 dimensions via Chern-Simons bosonic particle-vortex duality

Unlinking of Supercoiled DNA Catenanes by Type IIA Topoisomerases

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