MATH 467

Differentiable Manifolds

Full course information can be found here

The textbook for the course is: "An Introduction to Manifolds", by Loring W. Tu, Second Edition, Springer, (2010). ISBN 978-1-4419-7399-3

Suggested texts for supplementary reading include "Differential Topology: First Steps", by Andrew Wallace; "Topology from the Differential Viewpoint", by John Milnor; and "Introduction to Differentiable Manifolds", by Louis Auslander and Robert MacKenzie.

Syllabus for the course includes:

• Appendix A: Point-Set Topology.
• Chapter 1 Euclidean Spaces: Smooth Functions, Tangent Vectors as Derivations, Exterior Algebra of Multicovectors, Differential Forms
• Chapter 2 Manifolds: Smooth Manifolds; Smooth Maps, Quotient Spaces
• Chapter 3 Tangent Spaces: Tangent Space, Categories and Functors, Tangent Bundle; Vector Fields
• Chapter 4 Lie Groups and Lie Algebras
• Chapter 5 Differential Forms: 1-forms, k-forms, exterior derivative
• Chapter 6 Orientations, Integration on Manifolds
• Chapter 7 De Rham Theory

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