GTA Seminar: Zhu -- On Four-Manifolds With Positive Scalar Curvature

Speaker: Prof. Xi-Ping Zhu (Sun Yat-Sen University)

http://en.wikipedia.org/wiki/Zhu_Xiping

Time: Friday, Feb. 20, 11AM--12NOON 

Room: AGR Room, Carslaw 829.  

Lunch: after the talk. 

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Title: On Four-Manifolds With Positive Scalar Curvature

Abstract: it is well known that there exist several differentiable 
or topological obstructions to compact manifolds admitting metrics 
of positive scalar curvature. On the other hand, the family of 
manifolds with positive scalar curvature is quite large since any 
finite connected sum of them is still a manifold admitting a metric 
of positive scalar curvature. This talk is concerned with the 
classification question to this family.
          
The classical uniformization theorem implies that a two-dimensional 
compact manifold with positive scalar curvature is diffeomorphic to 
the sphere or the real projective space. The combination of works 
of Scheon-Yau and Perelman gives a complete classification to compact 
three-dimensional manifolds with positive scalar curvature. In this 
talk we will discuss how to extend Schoen-Yau-Perelman’s classification 
to four-dimension. This is based on the joint works with Bing-Long Chen 
and Siu-Hung Tang.

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Seminar website:

http://www.maths.usyd.edu.au/u/SemConf/Geometry/