Results 21 to 30 of about 34,079 (89)

Virtual knot groups and almost classical knots

, 2016
We define a group-valued invariant of virtual knots and relate it to various other group-valued invariants of virtual knots, including the extended group of Silver-Williams and the quandle group of Manturov and Bardakov-Bellingeri.
Boden, Hans U., Gaudreau, Robin, Harper, Eric, Nicas, Andrew J., White, Lindsay   +4 more
core   +1 more source

Virtual Knot Cobordism

, 2014
This paper defines a theory of cobordism for virtual knots and studies this theory for standard and rotational virtual knots and links. Non-trivial examples of virtual slice knots are given. Determinations of the four-ball genus of positive virtual knots
Kauffman, Louis H.
core   +1 more source

Knot Fertility and Lineage

, 2017
In this paper, we introduce a new type of relation between knots called the descendant relation. One knot $H$ is a descendant of another knot $K$ if $H$ can be obtained from a minimal crossing diagram of $K$ by some number of crossing changes. We explore
Cantarella, Jason, Henrich, Allison, Magness, Elsa, O'Keefe, Oliver, Perez, Kayla, Rawdon, Eric J., Zimmer, Briana   +6 more
core   +1 more source

Chern-Simons Theory in the Temporal Gauge and Knot Invariants through the Universal Quantum R-Matrix

, 2011
In temporal gauge A_{0}=0 the 3d Chern-Simons theory acquires quadratic action and an ultralocal propagator. This directly implies a 2d R-matrix representation for the correlators of Wilson lines (knot invariants), where only the crossing points of the ...
Alexander, Alexei Morozov, Alvarez, Alvarez, Alvarez, Alvarez, Andrey Smirnov, Baxter, Chari, Dimofte, Drinfeld, Drinfeld, Drinfeld, Dror, Dror, Dror, Dynnikov, Faddeev, Floreanini, Freyd, G, Gerasimov, Guadagnini, Guadagnini, Guadagnini, Guadagnini, Guadagnini, Guadagnini, Guadagnini, Guadagnini, Guadagnini, Jones, Jones, Jones, Kashaev, Kashaev, Kashaev, Kassel, Kassel, Kauffman, Kauffman, Kauffman, Kaul, Klimyk, Kontsevich, Labastida, Labastida, Labastida, Labastida, Labastida, Labastida, Majid, Morozov, Morozov, Morozov, Reidemeister, Reshetikhin, Reshetikhin, Schwarz, Smirnov, Turaev, Turaev, Turaev, Vassiliev, Witten, Wu   +65 more
core   +1 more source

Virtual Mosaic Knots [PDF]

, 2017
We extend mosaic knot theory to virtual knots and define a new type of knot: virtual mosaic knot. As in classical knots, Reidemeister moves are applied to a virtual mosaic knot to transform one knot diagram into another.
Garduno, Irina T.
core   +1 more source

A statistical approach to knot confinement via persistent homology. [PDF]

Proc Math Phys Eng Sci, 2022
Celoria D, Mahler BI.
europepmc   +1 more source

Dispersion braiding and band knots in plasmonic arrays with broken symmetries. [PDF]

Nanophotonics, 2023
Yin S, Alù A.
europepmc   +1 more source

Energy Landscapes of Model Knotted Polymers. [PDF]

J Chem Theory Comput
Hao T, Ge Y, Miller MA, L N Francesco A, Wales DJ.   +4 more
europepmc   +1 more source

Geometric learning of knot topology.

Soft Matter, 2023
Sleiman JL, Conforto F, Fosado YAG, Michieletto D.   +3 more
europepmc   +1 more source

Knot theory and error-correcting codes. [PDF]

Des Codes Cryptogr
Kılıç AB, Nijsten A, Pellikaan R, Ravagnani A.   +3 more
europepmc   +1 more source