First-order local invariants of stable maps from 3-manifolds to \(\mathbb R^{3}\)
The authors study Vassiliev type invariants of stable maps from 3-manifolds to \(\mathbb R^3\). These invariants are locally constant functions on the space of stable maps. The idea of Vassiliev invariants is to relate these functions with the topology of the discriminant set. The authors describe the codimension 1 and codimension 2 degenerations of (multi-) germs from 3-dimensions to 3-dimensions, and hence obtain a complete set of generators for first order Vassiliev invariants. Two of these invariants are related to monosingularities, one to a multisingularity, and one to the Euler charactersitic of a branch set. The authors also describe interesting relations to first order Vassiliev invariants of maps from 2-dimension to 3-dimension (found by Goryunov).
scientific article; zbMATH DE number 6141583
scientific article