10 problems

Let $L$ be a framed unoriented link with components $L_i$, and let $y_{\lambda_i}$ and $Q_{\lambda_i,\lambda_i}$ denote the corresponding Kauffman and Homfly annular decorations fo…

HOMFLY–PT–Kauffman factorisation criterion. If the HOMFLY–PT and Kauffman polynomials for a 2-component link $\mathcal{L}$ satisfy … .

Let $K$ be a knot, let $W_K$ be its Whitehead double, and let $F(K)$ be the Kauffman polynomial of $K$ in the variables $a$ and $z$. Stoimenow–Kidwell conjecture. Then … The questi…

Corrected HZ factorisability conjecture. If the HOMFLY–PT/Kauffman relation holds, then the HZ transform is factorisable:

Kauffman-polynomial span conjecture. The spans satisfy

Let $L$ be a solid torus link with wrapping number $\operatorname{wr}$, and let $\nabla_L$ denote its Kauffman polynomial. Wrapping-degree equality conjecture. … Equality holds for…

Let $\operatorname{BMW}^{\mathfrak{Leg}}_n$ be the Legendrian BMW algebra and let $\operatorname{BMW}^{\infty}_n$ be the specialized BMW algebra, with…

Let $K$ be a knot, let $\overline{K}$ denote its mirror image, and let $-\overline{K}$ denote the mirror image with reversed orientation. The Kauffman polynomial of $K$ is denoted…

Let ${\cal L}$ be an unoriented link with $L$ components, colored by representations $R_1,\ldots,R_L$. Let $\hat h_{R_1,\ldots,R_L}(t,\nu)$ and $\hat g_{R_1,\ldots,R_L}(t,\nu)$ be…

Let ${\cal K}$ be a knot, let $R$ be a representation, and let $\hat h_R(t,\nu)$ and $\hat g_R(t,\nu)$ be the reformulated colored Kauffman invariants obtained by applying the inve…