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

A note on the Mond conjecture and crosscap concatenations

“…(We consider complex analytic maps when K = C and smooth maps when K = R.) Some classifications of multigerms have been carried out as in [7], where Hobbs and Kirk classify certain multigerms from surfaces to R 3 using the complete transversal's method. Other classifications have been used in different contexts such as Vassiliev type invariants (see [6,14,2,3], for example), where multigerms up to codimension 2 are needed. However, the classical singularity theory techniques used to classify monogerms are hard to deal with when working with multigerms.…”