# LOSIK CLASSES FOR CODIMENSION-ONE FOLIATIONS

@article{Bazaikin2018LOSIKCF,
title={LOSIK CLASSES FOR CODIMENSION-ONE FOLIATIONS},
author={Ya.V. Bazaikin and Anton S. Galaev},
journal={arXiv: Differential Geometry},
year={2018}
}
• Published 2 October 2018
• Mathematics
• arXiv: Differential Geometry
Following Losik, for a codimension one foliation $\mathcal{F}$ on a smooth manifold $M$, two characteristic classes as elements of the cohomology $H^3(S(M/\mathcal{F})/\text{O}(1))$ and $H^2(S(M/\mathcal{F})/\text{GL}(1,\mathbb{R}))$, where $S(M/\mathcal{F})$ is the bundle of frames of infinite order over the leaf space $M/\mathcal{F}$, are considered; these classes are called here the Godbillon-Vey-Losik and the first Chern-Losik classes. The Godbillon-Vey-Losik class with values in \$H^3(S(M…
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