2002/04/10 by Christopher Deninger, Deninger, Christopher, Wilhelm Singhof +1
Mathematics · #37F75 #53C12 #58A14 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Finite Group Theory Research #K-Theory and Homology (math.KT) #math.CV #math.DG #math.KT #msc:37F75 #msc:53C12 #msc:58A14
paper · pdf · doi:10.48550/arxiv.math/0204111
to appear in Annals of Global Analysis and Geometry
arxiv created 2002/04/10 · openalex publication_date 2002/04/10 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 (\mathfrakg,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.