M. Golubitsky and D. Tischler
On the local stability of differential forms
Trans. AMS. 223 (1976) 205-221.
In this paper we determine which germs of differential s-forms on an n-manifold are stable (in the sense of Martinet). We show that when s neq 1 or when s = 1 and n < 5 Martinet had found almost all of the possible examples. The most interesting result states that for certain generic singularities of 1-forms on 4-manifolds an infinite dimensional moduli space occurs in the classification of the 1-forms with this given singularity type up to equivalence by pull-back via a diffeomorphism.