"Gysin sequence and Euler class of spherical Lie algebroids"

Publicationes Mathematicae, Debrecen, Tomus 59, (2001), Fasc. 3-4, 245-269.
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An n-dimensional Lie algebra g will be called a spherical Lie algebra if it is cohomologically equivalent to the n-sphere, i.e. Hⁱ(g) = 0 for 1 Ł i Ł n–1 and Hⁱ(g) = R for i = 0, n. The 1-dimensional abelian Lie algebra R and the 3-dimensional Lie algebras sl(2, R) and sk(3, R) are only such Lie algebras. This work deals with the invariantly oriented transitive Lie algebroids having spherical isotropy Lie algebras. The Lie algebroids of some principal bundles and of some TC-foliations are such algebroids. The aim of this work is to construct and investigate the Gysin sequence and the Euler class of such Lie algebroids by generalizing these notions introduced for R-Lie algebroids in [32].