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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.20778 |
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Table of Contents:
- Let $P$ be a pseudogroup of local diffeomorphisms of an $n$-dimensional smooth manifold $M$. Following Losik we consider characteristic classes of the quotient $M/P$ as elements of the de~Rham cohomology of the second order frame bundles over $M/P$ coming from the generators of the Gelfand-Fuchs cohomology. We provide explicit expressions for the classes that we call Godbillon-Vey-Losik class and the first Chern-Losik class. Reducing the frame bundles we construct bundles over $M/P$ such that the Godbillon-Vey-Losik class is represented by a volume form on a space of dimension $2n+1$, and the first Chern-Losik class is represented by a symplectic form on a space of dimension $2n$. Examples in dimension 2 are considered.