Real polarizable Hodge structures arising from foliations

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We construct real polarizable Hodge structures on the reduced leafwise cohomology of Kähler-Riemann foliations by complex manifolds. As in the classical case one obtains a hard Lefschetz theorem for this cohomology. Serre's Kählerian analogue of the Weil conjectures carries over as well. Generalizing a construction of Looijenga and Lunts one obtains possibly infinite dimensional Lie algebras attached to Kähler-Riemann foliations. Finally using $(\mathfrak{g},K)$-cohomology we discuss a class of examples obtained by dividing a product of symmetric spaces by a cocompact lattice and considering the foliations coming from the factors.
to appear in Annals of Global Analysis and Geometry

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Differential Geometry, Complex Variables, K-Theory and Homology, 37F75; 53C12; 58A14

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http://salesiana.dossiersoluciones.com/handle/123456789/63755

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0204111
 http://arxiv.org/abs/math/0204111

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arXiv