Time：16:00-17:00, Friday, Dec 2, 2022
Venue:E4-233, Yungu Campus & ZOOM
ZOOM ID:823 3635 2644
PASSCODE:478039
Host:Dr. Xing Gu, Institute for Theoretical Sciences, Westlake University
Speaker：Dr. Pengcheng Li, Southern University of Sicence and Technology
Biography:Doc. Pengcheng Li is a Postdoc researcher at the Southern University of Science and Technology, Shenzhen, China. In June 2020, He received his Ph.D. from the Academy of Mathematics and Systems Science, University of Chinese Academy of Sciences under the supervision of Professor Jianzhong PAN. His research interests are in algebraic topology, in particular the unstable homotopy theory of (n-1)-connected (n+2)-dimensional finite CW-complexes and its applications to geometry and physics.
Title：Suspension Homotopy of $4$-manifolds
Abstract：
In this talk we determine the homotopy type of the (double) suspension of a closed, smooth, connected, orientable $4$-manifold $M$, whose integral homology groups can have $2$-torsion.
This gives a complete solution to a prior research problem of So and Theriault.
Moreover, the decomposition results are applied to give a characterization of the second $2$-local cohomotopy set $\pi^2(M;\mathbb{Z}_{(2)})$, which is the set of homotopy classes of based maps from $M$ into the $2$-local sphere $S^2_{(2)}$.
