Square Numbers and the Alexander and Homfly Polynomial of Achiral Knots
نویسنده
چکیده
We examine and partially confirm some questions on properties of the the Alexander and HOMFLY polynomial of achiral knots. In particular we show that determinants of achiral knots are exactly the odd numbers representable as sums of two squares.
منابع مشابه
Square Numbers, Spanning Trees and Invariants of Achiral Knots
We examine and partially confirm some questions on properties of the the Alexander and HOMFLY polynomial of achiral knots. In particular we show that determinants of achiral knots are exactly the odd numbers representable as sums of two squares. Using the checkerboard coloring, then an analogous statement follows for the number of spanning trees in planar self-dual graphs.
متن کاملBraids, Transversal Knots and the Khovanov-rozansky Theory
We establish some inequalities about the Khovanov-Rozansky cohomologies of braids. These give new upper bounds of the self-linking numbers of transversal knots in standard contact S which is sharper than the well known bound given by the HOMFLY polynomial. We also introduce a sequence of transversal knot invariants, and discuss some of their properties.
متن کاملPolynomial Invariants of Legendrian Links and Plane Fronts
We show that the framed versions of the Kauuman and HOMFLY poly-nomials of a Legendrian link in the standard contact 3-space and solid torus are genuine polynomials in the framing variable. This proves a series of conjectures of 5] and provides estimates for the Bennequin{Tabachnikov numbers of such links. In a series of recent papers 1{3], V. I. Arnold revived interest in the study of plane cu...
متن کاملTopological BF theories in 3 and 4 dimensions
In this paper we discuss topological BF theories in 3 and 4 dimensions. Observables are associated to ordinary knots and links (in 3 dimensions) and to 2‐knots (in 4 dimensions). The vacuum expectation values of such observables give a wide range of invariants. Here we consider mainly the 3 dimensional case, where these invariants include Alexander polynomials, HOMFLY polynomials and Kontsevich...
متن کاملString theory and the Kauffman polynomial
We give a new, precise integrality conjecture for the colored Kauffman polynomial of knots and links inspired by large N dualities and the structure of topological string theory on orientifolds. According to this conjecture, the natural knot invariant to consider in an unoriented theory involves both the colored Kauffman polynomial and the colored HOMFLY polynomial for composite representations...
متن کامل