报告题目：Homotopy theory of gauge groups over high dimensional closed manifolds

报 告 人：黄瑞芝（中国科学院）

报告时间：2020.1.5 10:00-10:50

报告地点：数学中心 学术报告厅 （至善楼 234）

主 持 人：吴杰

摘 要：

The homotopy types of gauge groups have been investigated by many experts in the latest twenty years. So far the works mainly focus on bundles over 4-dimensional manifolds, the gauge theory of which plays an important role in Donaldson's theory. In this talk, we will discuss the homotopy theory of gauge groups over higher dimensional manifolds. In particular, we will discuss 3-families of high dimensional manifolds:

(1) (n-1)-connected 2n-manifolds, the classification of which was determined by

Wall and Freedman;

(2) sphere bundles over spheres based on the work of James and Whitehead;

(3) a family of non-simply-connected $5$-manifolds

We will show many homotopy decompositions of gauge groups under the mentioned cases. As the direct application, we will estimate the homotopy exponents of gauge groups. Besides, the methods here valid for rational cases as well.