Vassiliev Invariants from Symmetric Spaces

TL;DR

This paper introduces a new class of Vassiliev invariants derived from the curvature tensor of pseudo-Riemannian symmetric spaces, linking geometric structures to knot invariants.

Contribution

It constructs a natural framed weight system from symmetric space curvature tensors, characterizing Lie algebra weight systems with Riemann curvature symmetries.

Findings

Weight systems are of Lie algebra type.

They are characterized by Riemann curvature tensor symmetries.

Realized via holonomy Lie algebra action.

Abstract

We construct a natural framed weight system on chord diagrams from the curvature tensor of any pseudo-Riemannian symmetric space. These weight systems are of Lie algebra type and realized by the action of the holonomy Lie algebra on a tangent space. Among the Lie algebra weight systems, they are exactly characterized by having the symmetries of the Riemann curvature tensor.