scholarly journals Rozansky-Witten geometry of Coulomb branches and logarithmic knot invariants

2021 ◽  
pp. 104311
Author(s):  
Sergei Gukov ◽  
Po-Shen Hsin ◽  
Hiraku Nakajima ◽  
Sunghyuk Park ◽  
Du Pei ◽  
...  
Keyword(s):  
Knot Invariants

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.

ON FINITE TYPE 3-MANIFOLD INVARIANTS I

1996 ◽  
Vol 05 (04) ◽  
pp. 441-461 ◽  
Author(s):  
STAVROS GAROUFALIDIS
Keyword(s):  
Vector Space ◽  
Finite Type ◽  
Commutative Algebra ◽  
Integral Homology ◽  
Knot Invariants ◽  
Finite Type Invariants ◽  
Definition Of ◽  
Type 3

Recently Ohtsuki [Oh2], motivated by the notion of finite type knot invariants, introduced the notion of finite type invariants for oriented, integral homology 3-spheres. In the present paper we propose another definition of finite type invariants of integral homology 3-spheres and give equivalent reformulations of our notion. We show that our invariants form a filtered commutative algebra. We compare the two induced filtrations on the vector space on the set of integral homology 3-spheres. As an observation, we discover a new set of restrictions that finite type invariants in the sense of Ohtsuki satisfy and give a set of axioms that characterize the Casson invariant. Finally, we pose a set of questions relating the finite type 3-manifold invariants with the (Vassiliev) knot invariants.

scholarly journals Kontsevich’s integral for the Kauffman polynomial

1996 ◽  
Vol 142 ◽  
pp. 39-65 ◽  
Author(s):  
Thang Tu Quoc Le ◽  
Jun Murakami
Keyword(s):  
Finite Type ◽  
Knot Invariants ◽  
Chord Diagrams ◽  
Knot Invariant ◽  
Kauffman Polynomial ◽  
Zamolodchikov Equation

Kontsevich’s integral is a knot invariant which contains in itself all knot invariants of finite type, or Vassiliev’s invariants. The value of this integral lies in an algebra A0, spanned by chord diagrams, subject to relations corresponding to the flatness of the Knizhnik-Zamolodchikov equation, or the so called infinitesimal pure braid relations [11].

scholarly journals Generalized Equidistant Chebyshev Polynomials and Alexander Knot Invariants

2018 ◽  
Vol 63 (6) ◽  
pp. 488
Author(s):  
A. M. Pavlyuk
Keyword(s):  
Chebyshev Polynomials ◽  
Polynomial Invariants ◽  
Knot Invariants ◽  
Positive Integers

We introduce the generalized equidistant Chebyshev polynomials T(k,h) of kind k of hyperkind h, where k, h are positive integers. They are obtained by a generalization of standard and monic Chebyshev polynomials of the first and second kinds. This generalization is fulfilled in two directions. The horizontal generalization is made by introducing hyperkind ℎ and expanding it to infinity. The vertical generalization proposes expanding kind k to infinity with the help of the method of equidistant coefficients. Some connections of these polynomials with the Alexander knot and link polynomial invariants are investigated.

scholarly journals Knot invariants in 3-manifolds and essential tori

2001 ◽  
Vol 197 (1) ◽  
pp. 73-96 ◽  
Author(s):  
Paul Kirk ◽  
Charles Livingston
Keyword(s):  
Knot Invariants

scholarly journals A diagrammatic approach to link invariants of finite degree

2004 ◽  
Vol 94 (2) ◽  
pp. 295 ◽  
Author(s):  
Olof-Petter Östlund
Keyword(s):  
Finite Degree ◽  
Explicit Formulas ◽  
Connected Sum ◽  
Knot Invariants ◽  
Graphical Calculus ◽  
Link Invariants ◽  
Low Degree ◽  
Coalgebra Structure ◽  
Arrow Diagrams

In [5] M. Polyak and O. Viro developed a graphical calculus of diagrammatic formulas for Vassiliev link invariants, and presented several explicit formulas for low degree invariants. M. Goussarov [2] proved that this arrow diagram calculus provides formulas for all Vassiliev knot invariants. The original note [5] contained no proofs, and it also contained some minor inaccuracies. This paper fills the gap in literature by presenting the material of [5] with all proofs and details, in a self-contained form. Furthermore, a compatible coalgebra structure, related to the connected sum of knots, is introduced on the algebra of based arrow diagrams with one circle.

Knot invariants

1999 ◽  
pp. 167-189
Author(s):  
Kunio Murasugi ◽  
Bohdan I. Kurpita
Keyword(s):  
Knot Invariants

Linearized chord diagrams and an upper bound for vassiliev invariants

2000 ◽  
Vol 09 (07) ◽  
pp. 847-853 ◽  
Author(s):  
Béla Bollobás ◽  
Oliver Riordan
Keyword(s):  
Upper Bound ◽  
Knot Invariants ◽  
Vassiliev Invariants ◽  
Chord Diagrams

Recently, Stoimenow [J. Knot Th. Ram. 7 (1998), 93–114] gave an upper bound on the dimension dn of the space of order n Vassiliev knot invariants, by considering chord diagrams of a certain type. We present a simpler argument which gives a better bound on the number of these chord diagrams, and hence on dn.

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