Topological invariants of stable immersions of oriented 3-manifolds in \(\mathbb{R}^4\) (Q664646)

The authors present numerous detailed figures in their study of Vassiliev type invariants in the case of stable immersions of oriented 3-manifolds into \(\mathbb{R}^4\). They show that three topological invariants (the number of pairs of quadruple points and positive and negative linking invariants) form a complete set of generators of the \(\mathbb{Z}\)-module of first order local Vassiliev type invariants in this case. They describe the Euler characteristic of the immersed 3-manifold as a first order local invariant with a convenient expression in terms of the three generators. They also specify a new first order non-local Vassiliev type invariant, namely, the number of connected components of the triple points curve.