On the Lusternik-Schnirelman theory of a real cohomology class |
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Authors: | Email author" target="_blank">D?SchützEmail author |
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Institution: | (1) Mathematisches Institut, Westfälische Wilhelms-Universität Münster, Einsteinstr. 62, D-48149 Münster, Germany |
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Abstract: | Farber developed a Lusternik-Schnirelman theory for finite CW-complexes X and cohomology classes
H
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(X;). This theory has similar properties as the classical Lusternik-Schnirelman theory. In particular in 7] Farber defines a homotopy invariant cat(X,) as a generalization of the Lusternik-Schnirelman category. If X is a closed smooth manifold this invariant relates to the number of zeros of a closed 1-form representing . Namely, a closed 1-form representing which admits a gradient-like vector field with no homoclinic cycles has at least cat(X,) zeros. In this paper we define an invariant F(X,) for closed smooth manifolds X which gives the least number of zeros a closed 1-form representing can have such that it admits a gradient-like vector field without homoclinic cycles and give estimations for this number.
Mathematics Subject Classification (2000): Primary 37C29; Secondary 58E05 |
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Keywords: | |
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