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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



On the local stability of differential forms

Authors: Martin Golubitsky and David Tischler
Journal: Trans. Amer. Math. Soc. 223 (1976), 205-221
MSC: Primary 58A10; Secondary 58C25
MathSciNet review: 0431243
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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.

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Article copyright: © Copyright 1976 American Mathematical Society