Publication details

Non-diffeomorphic Reeb foliations and modified Godbillon-Vey class

Authors

BAZAIKIN Yaroslav V GALAEV Anton GUMENYUK Pavel

Year of publication 2022
Type Article in Periodical
Magazine / Source Mathematische Zeitschrift
Citation
Doi http://dx.doi.org/10.1007/s00209-021-02828-1
Keywords Reeb foliation; Reeb component; Leaf space of foliation; Characteristic classes of foliation; Gelfand formal geometry; Gelfand-Fuchs cohomology; Godbillon-Vey-Losik class
Description The paper deals with a modified Godbillon-Vey class defined by Losik for codimension-one foliations. This characteristic class takes values in the cohomology of the second order frame bundle over the leaf space of the foliation. The definition of the Reeb foliation depends upon two real functions satisfying certain conditions. All these foliations are pairwise homeomorphic and have trivial Godbillon-Vey class. We show that the modified Godbillon-Vey is non-trivial for some Reeb foliations and it is trivial for some other Reeb foliations. In particular, the modified Godbillon-Vey class can distinguish non-diffeomorphic foliations and it provides more information than the classical Godbillon-Vey class. We also show that this class is non-trivial for some foliations on the two-dimensional surfaces.

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