Winter 2015 -- Geometry and Topology 2 (Math 577)

Lectures are on Monday and Wednesday, 10:05--11:25 in Burnside 920
Alternate Time/Discussions are on Wednesday, 1-2pm, Burnside 1214

Syllabus

Final Exam: April 17, 9am-12pm, in Burnside Hall 1205
You'll be allowed to use a one-page crib sheet.

Lecture Notes

Scanned notes will be posted here as they become available. Numbering is logical, and does not necessarily agree with textbook. (J.Lee, Smooth Manifolds, 2nd Edition, available as e-book via McGill Library)

Chapter 1 (Preliminaries)
Chapter 2, §§ 2.1--2.2 (Differentiable manifolds: definitions, partition of unity)
Chapter 2, § 2.3 (Differentiable manifolds: tangent space)
Chapter 3 (Smooth maps, submersions, immersions, and embeddings)
Chapter 4 (Submanifolds, boundaries, and corners)
Chapter 5 (Tangent bundle, vector fields, and Sophus Lie)
Chapter 6 (Vector bundles, tensor algebra, Lie derivative)
Chapter 7 (Differential Forms and Integration, Stokes's Theorem)
Chapter 8, §§ 8.1--8.4 (Riemannian manifolds: Metrics and Connections)
Chapter 8, §§ 8.5--8.7 (Riemannian manifolds: Geodesics and Completeness)
Chapter 9 (DeRham cohomology, Mayer-Vietoris Theorem)

Homework Problems

Registered students are asked to work on the complete problem set at home, and contribute their solutions during the discussion session. Please note that your final grade depends in part on your participation in the discussion sessions.

Homework 1 to be discussed January 14
Homework 2 to be discussed January 21
Homework 3 to be discussed January 28
Homework 4 to be discussed February 11
Homework 5 to be discussed February 18

Midterm Homework 6 Your written solutions are due February 25, 1pm.
Solutions of Midterm Homework
Homework 7 to be discussed March 11
Homework 8 to be discussed March 25
Homework 9 to be discussed April 1st