On the local stability of differential forms

Golubitsky, Martin; Tischler, David

doi:10.1090/S0002-9947-1976-0431243-X

On the local stability of differential forms
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by Martin Golubitsky and David Tischler PDF

Trans. Amer. Math. Soc. 223 (1976), 205-221 Request permission

Abstract:

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 $s \ne 1$ or when $s = 1$ and $n \leqslant 4$ 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.

References

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Martin Golubitsky and David Tischler, The nonexistence of globally stable forms, Proc. Amer. Math. Soc. 58 (1976), 296–300. MR 415656, DOI 10.1090/S0002-9939-1976-0415656-3

On the stability of differential forms

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