Unités de Dirichlet et points critiques des 1-formes fermées

Translated title of the contribution: Dirichlet units and critical points of closed 1-forms

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S.P. Novikov developed an analog of the Morse theory for closed 1-forms. In this paper we suggest an analog of the Lusternik-Schnirelman theory for closed 1-forms. For any cohomology class ξ ∈ H1(X, R) we define an integer cl(ξ) (the cup-length associated with ξ); we prove that any closed 1-form representing ξ has at least cl(ξ) - 1 critical points. The number cl(ξ) is defined using cup-products in cohomology of some flat line bundles, such that their monodromy is described by complex numbers, which are not Dirichlet units.

Translated title of the contributionDirichlet units and critical points of closed 1-forms
Original languageFrench
Pages (from-to)695-700
Number of pages6
JournalComptes Rendus de l'Academie des Sciences - Series I: Mathematics
Issue number8
StatePublished - 15 Apr 1999


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