Holonomy Pseudogroups of Manifolds over Weil Algebras

Holonomy Pseudogroups of Manifolds over Weil Algebras

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 modelled on -modules of the type , where is a quotient algebra of . It is proved that the holonomy pseudogroup determines a complete -smooth manifo...

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Veröffentlicht in:Lobachevskii journal of mathematics 2023-04, Vol.44 (4), p.1494-1505
Hauptverfasser: Shurygin, V. V., Zubkova, S. K.
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Analysis
Geometry
Isomorphism
Manifolds
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
Probability Theory and Stochastic Processes
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Zusammenfassung: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 modelled on -modules of the type , where is a quotient algebra of . It is proved that the holonomy pseudogroup determines a complete -smooth manifold up to -diffeomorphism, and examples of application of holonomy pseudogroups are presented.
ISSN:1995-0802
1818-9962
DOI:10.1134/S1995080223040261