Real polarizable Hodge structures arising from foliations

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dc.creatorDeninger, Christopher
dc.creatorSinghof, Wilhelm
dc.date2002-04-10
dc.date.accessioned2026-07-07T04:47:32Z
dc.date.available2026-07-07T04:47:32Z
dc.descriptionWe 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.
dc.descriptionto appear in Annals of Global Analysis and Geometry
dc.identifierhttps://arxiv.org/abs/math/0204111
dc.identifierhttp://arxiv.org/abs/math/0204111
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/63755
dc.subjectDifferential Geometry
dc.subjectComplex Variables
dc.subjectK-Theory and Homology
dc.subject37F75; 53C12; 58A14
dc.titleReal polarizable Hodge structures arising from foliations
dc.typetext

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