Sergey A. Usanov

$\mathfrak{sl}(2)$-weight system does not extend to a graph 4-invariant

A long-standing question by S. Lando asks whether the $\mathfrak{sl}(2)$-weight system extends to a unique 4-invariant of graphs. We show that, in full generality, the answer to this question is negative. However, for certain specializations of the weight system, extensions do exist. Explicit formulae for computing two...