| BAZAIKIN, Yaroslav V, Anton GALAEV a Pavel GUMENYUK. Non-diffeomorphic Reeb foliations and modified Godbillon-Vey class. Mathematische Zeitschrift. Heidelberg: Springer Heidelberg, 2022, roč. 300, č. 2, s. 1335-1349. ISSN 0025-5874. Dostupné z: https://dx.doi.org/10.1007/s00209-021-02828-1. |
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@article{2362441,
author = {Bazaikin, Yaroslav V and Galaev, Anton and Gumenyuk, Pavel},
article_location = {Heidelberg},
article_number = {2},
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},
language = {eng},
issn = {0025-5874},
journal = {Mathematische Zeitschrift},
title = {Non-diffeomorphic Reeb foliations and modified Godbillon-Vey class},
volume = {300},
year = {2022}
}
TY - JOUR
ID - 2362441
AU - Bazaikin, Yaroslav V - Galaev, Anton - Gumenyuk, Pavel
PY - 2022
TI - Non-diffeomorphic Reeb foliations and modified Godbillon-Vey class
JF - Mathematische Zeitschrift
VL - 300
IS - 2
SP - 1335-1349
EP - 1335-1349
PB - Springer Heidelberg
SN - 00255874
KW - Reeb foliation
KW - Reeb component
KW - Leaf space of foliation
KW - Characteristic classes of foliation
KW - Gelfand formal geometry
KW - Gelfand-Fuchs cohomology
KW - Godbillon-Vey-Losik class
N2 - 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.
ER -
BAZAIKIN, Yaroslav V, Anton GALAEV a Pavel GUMENYUK. Non-diffeomorphic Reeb foliations and modified Godbillon-Vey class. \textit{Mathematische Zeitschrift}. Heidelberg: Springer Heidelberg, 2022, roč.~300, č.~2, s.~1335-1349. ISSN~0025-5874. Dostupné z: https://dx.doi.org/10.1007/s00209-021-02828-1.
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