The Kauffman-Vogel polynomials are three variable polynomial invariants of -valent rigid vertex graphs. A one-variable specialization of the Kauffman-Vogel polynomials for unoriented -valent rigid vertex graphs was given by using the Kauffman bracket and the Jones-Wenzl idempotent colored with . Bataineh, Elha…
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5 results for “Kauffman-Vogel”
This paper consists of three parts. First, we generalize the Jaeger Formula to express the Kauffman-Vogel graph polynomial as a state sum of the Murakami-Ohtsuki-Yamada graph polynomial. Then, we demonstrate that reversing the orientation and the color of a MOY graph along a simple circuit does not change the sl(N) Mur…
New invariants for Legendrian graphs defined and proven.
problem Defining and proving invariants for Legendrian graphs.
method Defined ruling invariants and proved their properties.
result Ruling invariants are compatible with vertex-identifying operations and vertical cuts/gluings.
We generalize the colored Jones polynomial to -valent graphs. This generalization is given as a sequence of invariants in which the first term is a one variable specialization of the Kauffman-Vogel polynomial. We use the invariant we construct to give a sequence of singular braid group representations.
We construct the first combinatorial 1-cocycle with values in the -module of isotopy classes of singular long knots in 3-space with a signed planar double point, and which represents a non trivial cohomology class in the topological moduli space of long knots. It can be interpreted as an invaria…