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| Autori principali: | , , |
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| Natura: | Preprint |
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2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2505.20778 |
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| _version_ | 1866910970363772928 |
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| author | Bazaikin, Yaroslav V. Efremenko, Yury D. Galaev, Anton S. |
| author_facet | Bazaikin, Yaroslav V. Efremenko, Yury D. Galaev, Anton S. |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_20778 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Losik classes of diffeomorphism pseudogroups Bazaikin, Yaroslav V. Efremenko, Yury D. Galaev, Anton S. Differential Geometry Geometric Topology 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. |
| title | On Losik classes of diffeomorphism pseudogroups |
| topic | Differential Geometry Geometric Topology |
| url | https://arxiv.org/abs/2505.20778 |