REGULAR HOMOTOPY AND VASSILIEV INVARIANTS OF GENERIC IMMERSIONS Sk → ℝ2k-1, k ≥ 4

Abstract

The regular homotopy class of a generic immersion Sk → ℝ2k-1 is calculated in terms of its self intersection manifold with natural additional structures. There is a natural notion of Vassiliev invariants of generic immersions. These may take values in any Abelian group G. It is proved that, for any m, the group of mth order G-valued invariants modulo invariants of lower order is isomorphic to G and that the Vassiliev invariants are not sufficient to separate generic immersions, which can not be obtained from each other by a regular homotopy through generic immersions.