Narrow Results

A necessary and sufficient algebraic condition for a diffeomorphism over a surface embedded in S³ to be induced by a regular homotopic deformation is discussed, and a formula for the number of signed pass moves needed for this regular homotopy is given.

The regular homotopy class of a generic immersion S^k → ℝ^2k-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 m^th 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.