Program
Riemannian Geometry on Four-Manifolds
Student No.:50
Time:Tue/Thu 18:30-20:00, 2013-09-26 ~ 2014-01-02 (except for public holidays)
Instructor:Abul Masood-ul-Alam  [Tsinghua University]
Place:Conference Room 3, Floor 2, Jin Chun Yuan West Building
Starting Date:2013-9-26
Ending Date:2014-1-2

 

 

Description:

The dimension four differs from higher dimensions in many respects. It is the first dimension Weyl curvature becomes non-trivial, quarternions come to play, rotation group SO(4) has non-trivial homomorphic images while SO(n), n>4 are simple or almost simple, Weyl tensor is decomposed into self-dual and anti-self-dual parts, Yang-Mills action is conformally invariant, and finally it is the dimension of our spacetime (we forget the metric signature for a moment). This course is mainly an effort to study Simon Salamon's "Topics in Four-Dimensional Riemannian Geometry (Lecture Notes in Mathematics vol. 1022, 1983)." Aim is to make the course suitable for both graduate and senior level undergraduate students in a self-contained way. We shall start with spheres, a review of group actions on manifolds, principal fibre bundles and some matrix groups.

 

Prerequisite:

Multivariable Calculus, Real Analysis, Linear Algebra and some basic knowledge of Riemannian Geometry (tensor, covariant derivative and curvature) or concurrent enrollment in a Riemannian Geometry or Relativity or Geometric Analysis course.