scholarly journals A Survey of Hyperbolic Knot Theory

2019 ◽  
pp. 1-30
Author(s):  
David Futer ◽  
Efstratia Kalfagianni ◽  
Jessica S. Purcell
Keyword(s):  
Knot Theory

QFT and unification of knot theories

2014 ◽  
Vol 29 (24) ◽  
pp. 1430025
Author(s):  
Alexey Sleptsov
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Knot Theory ◽  
Topological Quantum Field Theory ◽  
Quantum Field ◽  
Knot Invariants ◽  
Topological Quantum

We discuss relation between knot theory and topological quantum field theory. Also it is considered a theory of superpolynomial invariants of knots which generalizes all other known theories of knot invariants. We discuss a possible generalization of topological quantum field theory with the help of superpolynomial invariants.

Weight Systems from Feynman Diagrams

1998 ◽  
Vol 07 (01) ◽  
pp. 61-85 ◽  
Author(s):  
Dirk Kreimer
Keyword(s):  
Field Theory ◽  
Knot Theory ◽  
Feynman Diagrams ◽  
Weight System ◽  
Term Relation ◽  
Renormalization Theory

We find that the overall UV divergences of a renormalizable field theory with trivalent vertices fulfil a four-term relation. They thus come close to establish a weight system. This provides a first explanation of the recent successful association of renormalization theory with knot theory.

Disentangling Topological Puzzles by Using Knot Theory

2006 ◽  
Vol 79 (5) ◽  
pp. 368-375 ◽  
Author(s):  
Matthew Horak
Keyword(s):  
Knot Theory

COMPUTER AIDED KNOT THEORY USING MATHEMATICA AND MATHLINK

2002 ◽  
Vol 11 (06) ◽  
pp. 945-954 ◽  
Author(s):  
NORIKO IMAFUJI ◽  
MITSUYUKI OCHIAI
Keyword(s):  
Knot Theory ◽  
Computer Tool ◽  
The Public ◽  
Computer Aided ◽  
Data Files

We introduce a computer tool called Knot2000(K2K) which was developed for the purpose of support for the research of knot theory. K2K is a package on Mathematica in which consists of 19 functions and it has already been opened to the public with other external programs and data files. In this paper, we will describe focusing on the usages of each functions and some examples of effective ways to use K2K, and show its availability.

Applications to Knot Theory

2013 ◽  
pp. 101-131
Author(s):  
Joanna A. Ellis-Monaghan ◽  
Iain Moffatt
Keyword(s):  
Knot Theory

Totally knotted knots are prime

1982 ◽  
Vol 91 (3) ◽  
pp. 467-472
Author(s):  
J. C. Gomez-Larran¯aga
Keyword(s):  
Finite Number ◽  
Knot Theory ◽  
Piecewise Linear ◽  
Connected Sum ◽  
Higher Dimensional ◽  
The Family ◽  
Linear Category

Throughout, the word knot means a subspace of the 3-sphere S3 homeomorphic with the 1-sphere S1. Any knot can be expressed as a connected sum of a finite number of prime knots in a unique way (13), we consider the trivial knot a non-prime knot. (For higher dimensional knots, factorization and uniqueness have been studied in (1).) However given a knot it is difficult to determine if it is prime or not. We prove that totally knotted knots, see definition in §2, are prime in theorem 1, give a class of examples in theorem 2 and investigate how the last result can be applied to the conjecture that the family Y of unknotting number one knots are prime. (See problem 2 in (5).) At the end, prime tangles as defined by W. B. R. Lickerish are used to prove that in a certain family of knots, related somewhat to Y, there is just one non-prime knot: the square knot. The paper should be interpreted as being in the piecewise linear category. Standard definitions of 3-manifolds and knot theory may be found in (6) and (11) respectively.

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