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Area functionals and Godbillon-Vey cocycles. (English) Zbl 0759.57019
We investigate the natural domain of definition of the Godbillon-Vey 2- dimensional cohomology class of the group of diffeomorphisms of the circle. We introduce the notion of area functionals on a space of functions on the circle, we give a sufficiently large space of functions with nontrivial area functional and we give a sufficiently large group of Lipschitz homeomorphisms of the circle where the Godbillon-Vey class is defined.
Reviewer: T.Tsuboi

MSC:
57R32 Classifying spaces for foliations; Gelfand-Fuks cohomology
57R30 Foliations in differential topology; geometric theory
58H10 Cohomology of classifying spaces for pseudogroup structures (Spencer, Gelfand-Fuks, etc.)
26A45 Functions of bounded variation, generalizations
26B15 Integration of real functions of several variables: length, area, volume
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