Delta move and polynomial invariants of links
The delta move is an unknotting operation which substitutes a triangular entanglement by its rotation, introduced in [\textit{S. V. Matveev}, Mat. Zametki 42, 268--278 (1987; Zbl 0634.57006), resp., Math. Notes 42, 651--656 (1987; Zbl 0649.57010)], [\textit{H. Murakami} and \textit{Y. Nakanishi}, Math. Ann. 284, 75--89 (1989; Zbl 0646.57005)]. In this paper the authors give the relationship between the HOMFLY polynomials for the delta skein quadruple: namely the polynomials for the original oriented link \(L\), for the link \(M\) obtained by performing the delta move on \(L\), and smoothings \(L_0\) and \(M_0\), in the case that the arcs involved in the delta move belong to the same component. Using the relation, the authors also give the relationship between other finite type invariants for the quadruple. They further obtain a formula for the zero coefficient polynomials for the twist knots.
scientific article; zbMATH DE number 2136457
scientific article