Abstract
The notion of the holonomy pseudogroup on a total immersed transversal is extended to the case of complete foliated smooth manifolds over a Weil algebra \({\mathbf{A}}\) modelled on \({\mathbf{A}}\)-modules of the type \({\mathbf{A}}^{n}\oplus{\mathbf{B}}^{m}\), where \({\mathbf{B}}\) is a quotient algebra of \({\mathbf{A}}\). It is proved that the holonomy pseudogroup determines a complete \({\mathbf{A}}\)-smooth manifold up to \({\mathbf{A}}\)-diffeomorphism, and examples of application of holonomy pseudogroups are presented.
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The work of the second author is performed under the development program of Volga Region Mathematical Center (agreement no. 075-02-2023-944).
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(Submitted by M. A.Malakhaltsev)
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Shurygin, V.V., Zubkova, S.K. Holonomy Pseudogroups of Manifolds over Weil Algebras. Lobachevskii J Math 44, 1494–1505 (2023). https://doi.org/10.1134/S1995080223040261
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DOI: https://doi.org/10.1134/S1995080223040261