arXiv subjects
Publications and source records attributed to A. Kricker.
This is a list of open problems on invariants of knots and 3-manifolds with expositions of their history, background, significance, or importance. This list was made by editing open problems given in problem sessions in the workshop and seminars on `Invariants of Knots and 3-Manifolds' held at Kyoto in 2001.
We characterise the cabling operations on the weight systems of finite type knot invariants. The eigenvectors and eigenvalues of this family of operations are described over the cable eigenbasis. The action of immanent weight systems on general Feynman diagrams is considered, and the highest eigenvalue cabling eigenvectors are shown to be dual to the immanent weight systems. Using these results, we prove a recent conjecture of Bar-Natan and Garoufalidis on cablings of weight systems.
Previous work has shown that certain leading orders of arbitrary Vassiliev invariants are generically in the algebra of the coefficients of the Alexander-Conway polynomial \cite{KSA}. Here we illustrate this for a large class of examples, exposing the simple logic behind several existing results in the literature \cite{FKV,BNG}. This approach facilitates an extension to a large class of Lie (super)algebras.