MATH 467

Differentiable Manifolds

We will use the following books:

1"Differential Topology: First Steps", by Andrew Wallace;

2 "Topology from the Differential Viewpoint", by John Milnor; and

3"Introduction to Differentiable Manifolds", by Louis Auslander and Robert MacKenzie.

Syllabus for the course includes:

• Topological spaces
• Differentiable Manifolds; submanifolds
• Tangent spaces
• Critical points and levels
• Orientations
• Vector fields
• Tangent and Cotangent bundles
• Lie Groups
• Fiber Bundles
• Tensor Calculus
• Other topics as time permits
  

Course requirements include: weekly homework assignments; a midterm exam; and a final exam.