# 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} }

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…

## 4 Citations

Comparison of approaches to characteristic classes of foliations

- Mathematics
- 2017

Among classical approaches to the characteristic classes of foliations, there are two recent approaches: Crainic and Moerdijk defined the characteristic classes of a foliation as elements of the…

Product-type classes for vertex algebra cohomology of foliations on complex curves

- Mathematics
- 2021

We define a product of pairs of double complex spaces Cn m (V,W ,F) for gradig-restricted vertex algebra cohomology of codimension one foliation on a complex curve. We introduce a vertex algebra…

Characterization of codimension one foliations on complex curves by connections

- Mathematics
- 2021

A way to characterize the space of leaves of a foliation in terms of connections is proposed. A particular example of vertex algebra cohomology of codimension one foliations on complex curves is…

Non-diffeomorphic Reeb foliations and modified Godbillon-Vey class

- MathematicsMathematische Zeitschrift
- 2021

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 construct…

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