The subject of this paper is the notion of the connection in a regular Poisson manifold M, defined as a splitting of the Atiyah sequence of its Lie algebroid. In the case when the characteristic foliation F is an ℝ-Lie foliation, the fibre integral operator along the adjoint bundle is used to define the Euler class of the Poisson manifold M. When M is oriented 3-dimensional, the notion of the index of a local flat connection with singularities along a closed transversal is defined. If, additionally, F has compact leaves (then F is a fibration over ), an analogue of the Euler-Poincaré-Hopf index theorem for flat connections with singularities along closed transversals is obtained.
@article{bwmeta1.element.bwnjournal-article-bcpv51z1p141bwm,
author = {Kubarski, Jan},
title = {Connections in regular Poisson manifolds over $\mathbb{R}$-Lie foliations},
journal = {Banach Center Publications},
volume = {51},
year = {2000},
pages = {141-149},
zbl = {0981.53081},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv51z1p141bwm}
}
Kubarski, Jan. Connections in regular Poisson manifolds over ℝ-Lie foliations. Banach Center Publications, Tome 51 (2000) pp. 141-149. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv51z1p141bwm/
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