Contents

# Contents

## Idea

The Vassiliev skein relation is a way to extend knot invariants to singular knots (at least, to singular knots where the only singularities are double points). If $v$ is a knot invariant that takes values in an abelian group, then it is extended to singular knots using the relation

$v(L_d) = v(L_+) - v(L_-)$

where $L_d$ is a singular knot with a double point and $L_+$, respectively $L_-$, are formed from $L_d$ by replacing the double point by a positively oriented, respectively negatively oriented, crossing.

## References

General discussion:

Discussion in the context of quantization of 3d Chern-Simons theory:

category: knot theory

Last revised on September 10, 2022 at 03:11:19. See the history of this page for a list of all contributions to it.