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Mat. Zametki, 1996, Volume 59, Issue 2, Pages 303–310 (Mi mz1717)  

Ehresmann connection for the canonical foliation on a manifold over a local algebra

V. V. Shurygin

Kazan State University

Abstract: For a canonical foliation on a manifold $M^{\mathbb A}$ over a local algebra, the $\mathbb A$-affine horizontal distribution complementary to the leaves, similar to the horizontal distribution of a higher order connection on the fiber bundle of $\mathbb A$-jets, is defined. In the case of a complete manifold $M^{\mathbb A}$, the $\mathbb A$-affine horizontal distribution is proved to be an Ehresmann connection in the sense of Blumental–Hebda. It is shown that the $\mathbb A$-affine horizontal distribution on $M^{\mathbb A}$ exists if and only if the Atiyah class of a certain foliated principal bundle vanishes.

DOI: https://doi.org/10.4213/mzm1717

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English version:
Mathematical Notes, 1996, 59:2, 213–218

Bibliographic databases:

UDC: 514.76
Received: 17.05.1993

Citation: V. V. Shurygin, “Ehresmann connection for the canonical foliation on a manifold over a local algebra”, Mat. Zametki, 59:2 (1996), 303–310; Math. Notes, 59:2 (1996), 213–218

Citation in format AMSBIB
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\by V.~V.~Shurygin
\paper Ehresmann connection for the canonical foliation on a~manifold over a~local algebra
\jour Mat. Zametki
\yr 1996
\vol 59
\issue 2
\pages 303--310
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\crossref{https://doi.org/10.4213/mzm1717}
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\transl
\jour Math. Notes
\yr 1996
\vol 59
\issue 2
\pages 213--218
\crossref{https://doi.org/10.1007/BF02310963}
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