Manifolds and Lie Groups

Instructor: Guanghua JI

Classroom and Time: B115, ZhiXin Building/ 5-6, Mon Wed

Prerequisites: general topology, functional analysis, group theory

Grading: The course grade will be based homework(50%) and final exam(50%).

References:

  1 Loring W. Tu, An Introduciton to Manifolds, Springer.

  2 F. Warner, Foundations of Differentiable Manifolds and Lie Groups, GTM 94.

  3 John M. Lee, Introduction to Smooth Manifolds, GTM 218.

Syllabus:

  Chapter I, Eclidean Spaces

  Chapter II, Smooth Manifolds

  Chanter III, The Tangent Space

  Chapter IV, Lie Groups and Lie Algebras

  Chapter V, Differential Forms

  Chapter VI, Integration

  Chapter VII, De Rham Theory