- Tytuł:
- Connections in regular Poisson manifolds over ℝ-Lie foliations
- Autorzy:
- Kubarski, Jan
- Powiązania:
- https://bibliotekanauki.pl/articles/1207678.pdf
- Data publikacji:
- 2000
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
Lie algebroid
ℝ-Lie foliation
Poisson manifold
closed transversal
flat connection with singularites along closed transversals - Opis:
- 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 $S^{1}$), an analogue of the Euler-Poincaré-Hopf index theorem for flat connections with singularities along closed transversals is obtained.
- Źródło:
-
Banach Center Publications; 2000, 51, 1; 141-149
0137-6934 - Pojawia się w:
- Banach Center Publications
- Dostawca treści:
- Biblioteka Nauki
Artykuł