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On Losik Classes of Diffeomorphism Pseudogroups. / Bazaikin, Yaroslav V.; Efremenko, Yury D.; Galaev, Anton S.

в: Results in Mathematics, Том 80, № 8, 235, 12.11.2025.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

Harvard

Bazaikin, YV, Efremenko, YD & Galaev, AS 2025, 'On Losik Classes of Diffeomorphism Pseudogroups', Results in Mathematics, Том. 80, № 8, 235. https://doi.org/10.1007/s00025-025-02553-9

APA

Bazaikin, Y. V., Efremenko, Y. D., & Galaev, A. S. (2025). On Losik Classes of Diffeomorphism Pseudogroups. Results in Mathematics, 80(8), [235]. https://doi.org/10.1007/s00025-025-02553-9

Vancouver

Bazaikin YV, Efremenko YD, Galaev AS. On Losik Classes of Diffeomorphism Pseudogroups. Results in Mathematics. 2025 нояб. 12;80(8):235. doi: 10.1007/s00025-025-02553-9

Author

Bazaikin, Yaroslav V. ; Efremenko, Yury D. ; Galaev, Anton S. / On Losik Classes of Diffeomorphism Pseudogroups. в: Results in Mathematics. 2025 ; Том 80, № 8.

BibTeX

@article{75c7366a5d1f462f9812803893a311af,
title = "On Losik Classes of Diffeomorphism Pseudogroups",
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.",
keywords = "Diffeomorphism pseudogroup, Gelfand formal geometry, Gelfand-Fuchs cohomology, Godbillon-Vey-Losik class, characteristic classes",
author = "Bazaikin, {Yaroslav V.} and Efremenko, {Yury D.} and Galaev, {Anton S.}",
note = "A.G. was supported by the grant 24-10031K of the Czech Science Foundation (GA{\v C}R).",
year = "2025",
month = nov,
day = "12",
doi = "10.1007/s00025-025-02553-9",
language = "English",
volume = "80",
journal = "Results in Mathematics",
issn = "1422-6383",
publisher = "Birkhauser Verlag Basel",
number = "8",

}

RIS

TY - JOUR

T1 - On Losik Classes of Diffeomorphism Pseudogroups

AU - Bazaikin, Yaroslav V.

AU - Efremenko, Yury D.

AU - Galaev, Anton S.

N1 - A.G. was supported by the grant 24-10031K of the Czech Science Foundation (GAČR).

PY - 2025/11/12

Y1 - 2025/11/12

N2 - 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.

AB - 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.

KW - Diffeomorphism pseudogroup

KW - Gelfand formal geometry

KW - Gelfand-Fuchs cohomology

KW - Godbillon-Vey-Losik class

KW - characteristic classes

UR - https://www.scopus.com/pages/publications/105021518742

UR - https://www.mendeley.com/catalogue/d60cfbea-eb84-348f-9b18-f64f673c4367/

U2 - 10.1007/s00025-025-02553-9

DO - 10.1007/s00025-025-02553-9

M3 - Article

VL - 80

JO - Results in Mathematics

JF - Results in Mathematics

SN - 1422-6383

IS - 8

M1 - 235

ER -

ID: 72229789