Holonomy pseudogroups as obstructions to equivalence of manifolds over the algebra of dual numbers
A smooth manifold over the algebra of dual numbers D (a D-smooth manifold) carries the canonical foliation whose leaves are affine manifolds. Extension of charts on a D-smooth manifold along leaf paths allows ones to associate with an immersed transversal of the canonical foliation a pseudogroup of...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Kazan Federal University
2019-09-01
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| Series: | Учёные записки Казанского университета: Серия Физико-математические науки |
| Subjects: | |
| Online Access: | https://kpfu.ru/uz-eng-phm-2019-3-9.html |
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| Summary: | A smooth manifold over the algebra of dual numbers D (a D-smooth manifold) carries the canonical foliation whose leaves are affine manifolds. Extension of charts on a D-smooth manifold along leaf paths allows ones to associate with an immersed transversal of the canonical foliation a pseudogroup of local D-diffeomorphisms called the holonomy pseudogroup. In the present paper, holonomy pseudogroups are applied to the study of D-diffeomorphisms between quotient manifolds of the algebra by lattices. In particular, it is shown that a D-diffeomorphism between two such manifolds exists if and only if one of the lattices is obtained from the other by the multiplication by a dual number. In addition, it is shown that some D-smooth manifolds naturally associated with an affine manifold are D-diffeomorphic if and only if this manifold is radiant. |
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| ISSN: | 2541-7746 2500-2198 |