Topological invariants of stable immersions of oriented 3-manifolds in R4

We show that the Z-module of first order local Vassiliev type invariants of stable immersions of oriented 3-manifolds into R4 is generated by 3 topological invariants: The number of pairs of quadruple points and the positive and negative linking invariants ℓ+ and ℓ− introduced by V. Goryunov (1997) [7]. We obtain the expression for the Euler characteristic of the immersed 3-manifold in terms of these invariants. We also prove that the total number of connected components of the triple points curve is a non-local Vassiliev type invariant.