Abstract
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 ε H 1( 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.
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