Add to ORKGAbstract. The Kontsevich integral is decomposed into two parts; one part depends on overpass or underpass of the crossing of a knot while the other depends only on the plane curve obtained by projecting the knot to the plane. In this paper, firstly, we express the latter part in terms of Arnold’s invariants of plane curves J+, J − and St up to degree three. Secondly, we show that the Gauss diagram formulas for the Kontsevich integral agree with other types of formulas for Vassiliev invariants which are introduced by M. Polyak and O. Viro. 1
Using elementary equalities between various cables of the unknot and the Hopf link, we prove the Whe...
In [5] M. Polyak and O. Viro developed a graphical calculus of diagrammatic formulas for Vassiliev l...
AbstractA formula for computing the Milnor (concordance) invariants from the Kontsevich integral is ...
The Kontsevich integral is decomposed into two parts; one part depends on overpass or underpass of t...
Vassiliev’s invariants seem to be a very promising set of knot invariants to classify knot types. Al...
We review quantum field theory approach to the knot theory. Using holomorphic gauge, we obtain the K...
. We use a notion of chord diagrams to define their representations in Gauss diagrams of plane curve...
AbstractWe use a notion of chord diagrams to define their representations in Gauss diagrams of plane...
AbstractThe Kontsevich integral of a knot is a graph-valued invariant which (when graded by the Vass...
and examples of computation. Finally, in Section 3 we discuss three operations on knots --- mutation...
AbstractWe study the unwheeled rational Kontsevich integral of torus knots. We give a precise formul...
The Kontsevich integral of a knot is a graph-valued invariant which (when graded by the Vassiliev de...
We use an example to provide evidence for the statement: the Vassiliev-Kontsevich invariants kn of a...
. We conjecture an exact formula for the Kontsevich integral of the unknot, and also conjecture a fo...
This book provides an accessible introduction to knot theory, focussing on Vassiliev invariants, qua...
Using elementary equalities between various cables of the unknot and the Hopf link, we prove the Whe...
In [5] M. Polyak and O. Viro developed a graphical calculus of diagrammatic formulas for Vassiliev l...
AbstractA formula for computing the Milnor (concordance) invariants from the Kontsevich integral is ...
The Kontsevich integral is decomposed into two parts; one part depends on overpass or underpass of t...
Vassiliev’s invariants seem to be a very promising set of knot invariants to classify knot types. Al...
We review quantum field theory approach to the knot theory. Using holomorphic gauge, we obtain the K...
. We use a notion of chord diagrams to define their representations in Gauss diagrams of plane curve...
AbstractWe use a notion of chord diagrams to define their representations in Gauss diagrams of plane...
AbstractThe Kontsevich integral of a knot is a graph-valued invariant which (when graded by the Vass...
and examples of computation. Finally, in Section 3 we discuss three operations on knots --- mutation...
AbstractWe study the unwheeled rational Kontsevich integral of torus knots. We give a precise formul...
The Kontsevich integral of a knot is a graph-valued invariant which (when graded by the Vassiliev de...
We use an example to provide evidence for the statement: the Vassiliev-Kontsevich invariants kn of a...
. We conjecture an exact formula for the Kontsevich integral of the unknot, and also conjecture a fo...
This book provides an accessible introduction to knot theory, focussing on Vassiliev invariants, qua...
Using elementary equalities between various cables of the unknot and the Hopf link, we prove the Whe...
In [5] M. Polyak and O. Viro developed a graphical calculus of diagrammatic formulas for Vassiliev l...
AbstractA formula for computing the Milnor (concordance) invariants from the Kontsevich integral is ...