Dirichlet Units and Critical Points of Closed 1 – Forms


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 cuplength associated with ξ); we prove that any closed 1-form representing ξ has at least cl(ξ)− 1 critical points. The… (More)