Basic Cohomology of Moment-Angle Manifolds

Explore the intricacies of moment-angle manifolds in this 37-minute lecture by Roman Krutowski from UCLA. Delve into the construction of complex moment-angle manifolds from complete fans and their canonical holomorphic foliations. Learn how these structures generalize toric varieties for non-rational fans. Discover the main result: a Davis-Januszkiewicz type formula for calculating basic de Rham and Dolbeault cohomology of these foliations. Understand the isomorphism involving ideals reconstructed from fan data, as conjectured by Battaglia and Zaffran and proven in collaborative works with Ishida and Panov. Follow the lecture's progression from introduction through canonical foundations, basic cohomology, theorem presentation, isomorphism explanation, to the generalization of toric variety cohomology rings.