1996
DOI: 10.1090/s0002-9947-96-01646-7
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Bott’s vanishing theorem for regular Lie algebroids

Abstract: Abstract. Differential geometry has discovered many objects which determine Lie algebroids playing a role analogous to that of Lie algebras for Lie groups. For example:-differential groupoids, -principal bundles, -vector bundles, -actions of Lie groups on manifolds, -transversally complete foliations, -nonclosed Lie subgroups, -Poisson manifolds, -some complete closed pseudogroups. We carry over the idea of Bott's Vanishing Theorem to regular Lie algebroids (using the Chern-Weil homomorphism of transitive Lie … Show more

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Cited by 15 publications
(16 citation statements)
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References 6 publications
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“…, where X ′ and Y ′ have (f := f k )-decompositions (8) and (9). In the same way as in the case k = 1 it follows that f k is an anchored vector bundle morphism.…”
Section: Morphisms Of Vector Bundles With Differentials Consider Nowmentioning
confidence: 66%
See 2 more Smart Citations
“…, where X ′ and Y ′ have (f := f k )-decompositions (8) and (9). In the same way as in the case k = 1 it follows that f k is an anchored vector bundle morphism.…”
Section: Morphisms Of Vector Bundles With Differentials Consider Nowmentioning
confidence: 66%
“…In the same way, if k ∈ IN , p ∈ IN * and X ′ , Y ′ ∈ θ ′(k) , where k = max(deg X ′ , deg Y ′ ) have (f := f k )-decompositions (8) and 9respectively, then…”
Section: Morphisms Of Vector Bundles With Differentials Consider Nowmentioning
confidence: 95%
See 1 more Smart Citation
“…known as the Atiyah sequence of the regular Lie algebroid A ( [11]). The differential D ∇ A (3.5) can be simplified if we choose a special linear connection on the regular Lie algebroid A.…”
Section: Linear Extension Of the Anchor Map ρmentioning
confidence: 99%
“…of Lie algebroids over M (cf. [11]). The main purpose of this paper is to investigate whether Atiyah classes of dg manifolds arising from regular Lie algebroids respect the above Atiyah sequence.…”
Section: Introductionmentioning
confidence: 99%