Event Type:

Geometry-Topology Seminar

Date/Time:

Monday, November 21, 2016 - 12:00 to 12:45

Location:

Gilkey 115

Institution:

Graduate Student

Abstract:

In this second talk, firstly we will mention how the topology of the group of isometries on a Riemannian manifold will be affected by the curvature, and vice versa. Then we will turn to some powerful results regarding to the fixed point set of an isometry group action. These results lead to a general obstruction theorem of positively curve manifold: the theorem by Synge. At last, we will discuss the proof of the Hsiang-Kleiner's theorem, which gives a nice classification of compact, positively curved 4-manifolds admitting circle action.