"The Euler-Poincare-Hopf theorem for some regular R-Lie algebroids"

"Proceedings of the I Colloquium on Lie Theory and Applications",Vigo, SPAIN, 17-22 July, 2000. University of Vigo, 2002 (in print).
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An analogue of the Euler-Poincare-Hopf theorem for sphere bundles is obtained for some regular Lie algebroids including Lie algebroids of some Poisson 3-manifolds over R-Lie foliations. Flat connections with singularities along closed transversals play a role of cross-sections of sphere bundles.