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… 
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References

SHOWING 1-10 OF 48 REFERENCES
Dynamics and the Godbillon-Vey Class of C^1 Foliations
Let F be a codimension-one, C^2-foliation on a manifold M without boundary. In this work we show that if the Godbillon--Vey class GV(F) \in H^3(M) is non-zero, then F has a hyperbolic resilient leaf.
The dynamics of open, foliated manifolds and a vanishing theorem for the Godbillon-Vey class
Let (M,.F) be a C3-foliated n-manifold with leaves of dimension n 1. Let gv(F) E H3(M, IR) denote the characeristic class introduced by Godbillon and Vey in [G-V]. Considerable effort has been made
Secondary classes and transverse measure theory of a foliation
1. The purpose of this note is to announce several theorems showing how the secondary classes of a foliation J of a compact manifold X depend upon the measure theoretic properties of the equivalence
Comparison of approaches to characteristic classes of foliations
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
Orbit spaces and leaf spaces of foliations as generalized manifolds
The paper gives a categorical approach to generalized manifolds such as orbit spaces and leaf spaces of foliations. It is suggested to consider these spaces as sets equipped with some additional
On the centralizer of diffeomorphisms of the half-line
Let f be a smooth diffeomorphism of the half-line fixing only the origin and Z^r its centralizer in the group of C^r diffeomorphisms. According to well-known results of Szekeres and Kopell, Z^1 is a
HOMOGENEOUS SPACES OF INFINITE-DIMENSIONAL LIE ALGEBRAS AND CHARACTERISTIC CLASSES OF FOLIATIONS
In this article we introduce a new language to describe many problems of differential geometry: for example, problems connected with the theory of pseudogroups, Lie equations, foliations,
Čech-De Rham theory for leaf spaces of foliations
We present a new ‘‘Čech-De Rham’’ model for the cohomology of the classifying space of a foliated manifold. This model enables us to lift the construction of known characteristic classes in the
A connectedness result for commuting diffeomorphisms of the interval
  • Helene Eynard
  • Mathematics
    Ergodic Theory and Dynamical Systems
  • 2010
Abstract Let 𝒟r+[0,1], r≥1, denote the group of orientation-preserving 𝒞r diffeomorphisms of [0,1]. We show that any two representations of ℤ2 in 𝒟r+[0,1], r≥2, are connected by a continuous path
Normal forms for certain singularities of vectorfields
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