Time: 13:00-15:00, Tuesday, June 30 2026
Venue: E14-212, Yungu Campus
Speaker: Prof. Yi Lin, Georgia Southern University
Title: Transverse Geometry and the de Rham Cohomology of Non-Hausdorff Homogeneous Spaces
Abstract: A fundamental tool in classical equivariant geometry is the averaging operator over a compact Lie group, which replaces closed differential forms by invariant representatives without changing their cohomology classes. In this talk, I will construct a transverse analogue of this operator for isometric transverse Lie algebra actions on Riemannian foliations. The construction is entirely infinitesimal and draws on Molino theory, Sergiescu’s transverse integration, and basic Poincaré duality, under a natural compactness assumption on the leaf-closure space.
As a main application, I will use the transverse averaging operator to compute the basic cohomology of Lie foliations of compact type. I will then apply this computation to the diffeological de Rham cohomology of homogeneous spaces G/H, where G need not be compact and H is a connected Lie subgroup that need not be closed. This extends the classical Chevalley–Eilenberg description beyond its traditional setting and provides a cohomological framework for certain non-Hausdorff homogeneous spaces.
