报告人： Yi Lin (Georgia Southern University)
时间：2018年6月6日，星期三，14：00－15：00.
地点：精正楼2楼报告厅
题目： Localization formula for Riemannian foliations
摘要： A Riemannian foliation is a foliation on a smooth manifoldthat comes equipped with a transverse Riemannian metric: a fiberwise Riemannianmetric g on the normal bundle of the foliation, such that for any vector fieldX tangent to the leaves, the Lie derivative L(X)g=0. In this talk, wewould discuss the notion of transverse Lie algebra actions on Riemannian foliations,which is used as a model for Lie algebra actions on the leave space of afoliation. Using an equivariant version of the basic cohomology theory onRiemannian foliations, we explain that when the action preserves the transverseRiemannian metric, there is a foliated version of the classicalBorel-Atiyah-Segal localization theorem. Using the transverse integrationtheory for basic forms on Riemannian foliations, we would also explain how toestablish a foliated version of the Atiyah-Bott-Berline-Vergne integrationformula, which reduce the integral of an equivariant basic cohomology class toan integral over the set of invariant leaves. This talk is based on a veryrecent joint work with Reyer Sjamaar.