Abstract

Key spaces in Toric Topology refer to a family of spaces that carry torus actions. They include moment-angle complexes, toric manifolds and orbifolds, partial quotients, and their real analogs. The study of toric spaces also stimulates the development of polyhedral products. In three talks, we aim to cover the following topics: 1) the fundamental properties of these key spaces, 2) tools for computing their cohomologies, and 3) homotopy theory of polyhedral products.