11 citations · 42 across the 9 of their papers we have counts for
9 papers
Khovanov complexes for bipartite links
A. Anokhina, E. Lanina, A. Morozov
Recently, for a limited class for bipartite links, the complicated Khovanov-Rozansky matrix factorization technique was reduced to an analogue of elementary Kauffman-Khovanov cycle…
Operator lift of Reshetikhin-Turaev formalism to Khovanov-Rozansky TQFTs
Dmitry Galakhov, Elena Lanina, Alexei Morozov
Topological quantum field theory (TQFT) is a powerful tool to describe homologies, which normally involve complexes and a variety of maps/morphisms, what makes a functional integra…
Analogue of Goeritz matrices for computation of bipartite HOMFLY-PT polynomials
A. Anokhina, D. Korzun, E. Lanina +1
The Goeritz matrix is an alternative to the Kauffman bracket and, in addition, makes it possible to calculate the Jones polynomial faster with some minimal choice of a checkerboard…
Khovanov-Rozansky cycle calculus for bipartite links
A. Anokhina, E. Lanina, A. Morozov
Bipartite calculus is a direct generalization of Kauffman planar expansion from to arbitrary , applicable to the restricted class of knots which are entirely made of antip…
Bipartite expansion beyond biparticity
A. Anokhina, E. Lanina, A. Morozov
The recently suggested bipartite analysis extends the Kauffman planar decomposition to arbitrary , i.e. extends it from the Jones polynomial to the HOMFLY polynomial. This provi…
Planar decomposition of bipartite HOMFLY polynomials in symmetric representations
A. Anokhina, E. Lanina, A. Morozov
We generalize the recently discovered planar decomposition (Kauffman bracket) for the HOMFLY polynomials of bipartite knot/link diagrams to (anti)symmetrically colored HOMFLY polyn…
Planar decomposition of the HOMFLY polynomial for bipartite knots and links
A. Anokhina, E. Lanina, A. Morozov
The theory of the Kauffman bracket, which describes the Jones polynomial as a sum over closed circles formed by the planar resolution of vertices in a knot diagram, can be straight…
Towards tangle calculus for Khovanov polynomials
A. Anokhina, E. Lanina, A. Morozov
We provide new evidence that the tangle calculus and "evolution" are applicable to the Khovanov polynomials for families of long braids inside the knot diagram. We show that jumps…
Defect and degree of the Alexander polynomial
E. Lanina, A. Morozov
Defect characterizes the depth of factorization of terms in differential (cyclotomic) expansions of knot polynomials, i.e. of the non-perturbative Wilson averages in the Chern-Simo…