叶理引起的实可极化霍奇结构
Real polarizable Hodge structures arising from foliations
摘要：
我们利用复流形在Kähler-Riemann叶理的约化叶上同调上构造了实可极化Hodge结构.在经典的情况下，人们得到一个硬莱夫谢茨定理，这个上同调。塞尔的凯勒式的韦伊结构也延续了下来。推广Looijenga和Lunts的一个构造，我们得到了可能的无限维李代数，它依附于Kähler-Riemann叶状结构。最后，利用$(\mathfrak{g},K)$ -上同调，讨论了对称空间的乘积除以余紧格并考虑因子的叶理所得到的一类例子。
英文摘要：
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.
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