Real polarizable Hodge structures arising from foliations
微分几何
2007-05-23 v1 复变函数
K理论与同调
摘要
We construct real polarizable Hodge structures on the reduced leafwise cohomology of K\"ahler-Riemann foliations by complex manifolds. As in the classical case one obtains a hard Lefschetz theorem for this cohomology. Serre's K\"ahlerian 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 K\"ahler-Riemann foliations. Finally using -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.
引用
@article{arxiv.math/0204111,
title = {Real polarizable Hodge structures arising from foliations},
author = {Christopher Deninger and Wilhelm Singhof},
journal= {arXiv preprint arXiv:math/0204111},
year = {2007}
}
备注
to appear in Annals of Global Analysis and Geometry