>>11408780Vasiliev invariants can be used to label the topological vacuua in (2D+1)CFT.
https://www.semanticscholar.org/paper/Vassiliev-invariants-and-de-Rham-complex-on-the-of-Kohno/cc9d910fe4836cb6bbb4015758ceef8e7e2628a9This labeling allows a state-sum construction for the partition function in a TQFT, since then you may transform summation over coloured ribbon graphs into a summation over these invariants classifying such graphs. By treating as a trace of the Gibbs measure over the ground states, each invariant then labels distinct ground state in the quantum theory.
In this interpretation, more sophisticated invariants such as Chern, Postnikov, Atiyah-Bott-Shapiro, Pontrjagyn and Arf-Kervaire-Brown can all be realized as topological vacuua.
