Smooth maps with singularities of bounded K-codimensions

Abstract

We will prove the relative homotopy principle for smooth maps with singularities of a given {\cal K}-invariant class with a mild condition. We next study a filtration of the group of homotopy self-equivalences of a given manifold P by considering singularities of non-negative {\cal K}-codimensions.

Typographic errors are revised and several expressions are modified to better ones