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arXiv · 2505.20778

On Losik classes of diffeomorphism pseudogroups

Yaroslav V. Bazaikin·Yury D. Efremenko·Anton S. Galaev
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Abstract

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.

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Yaroslav V. Bazaikin, Yury D. Efremenko, Anton S. Galaev. 2025-05-27. On Losik classes of diffeomorphism pseudogroups. https://arxiv.org/abs/2505.20778

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