Time：15:00, Thursday, November 21, 2022
Venue: E4-201
Speaker: Yichen Tong, Institute for Theoretical Sciences
Title: On homotopy commutativity
Abstract: A fundamental problem in homotopy theory is determining whether a given H-space is homotopy commutative. In particular, there are few results regarding the loop spaces of finite complexes, including those of closed manifolds. The cases for spheres were successfully solved as the famous Hopf invariant one problem, and the complex and quaternion projective spaces were studied by Ganea in 1967. A quasitoric manifold is a topological counterpart of a smooth projective toric variety, with complex projective spaces serving as classical examples. Similar to a toric variety, any quasitoric manifold can be constructed by certain combinatorial data. In this talk, I will present an equivalent condition for homotopy commutativity in quasitoric manifolds in terms of the corresponding combinatorial data, which partially generalizes Ganea's result.
This talk is based on joint work with Hasui, Kishimoto and Tsutaya.
