18.965: Differential Geometry, Fall 2007

Monday Wednesday Friday 2pm-3pm, room 2-255... starting Wednesday September 5.

Instructor: Marco Gualtieri [] office 2-171

Suggested prerequisite: Analysis II (18.101) and Algebraic Topology I (18.905)

Main text: Warner's "Foundations of differentiable manifolds and Lie groups" ISBN 0387908943.

Secondary texts:

• Lee's "Introduction to Smooth Manifolds" ISBN 0387954481.
• Milnor's "Morse theory" ISBN 0691080089
• Wells' "Differential Analysis on Complex Manifolds" ISBN 0387904190
• Bott & Tu's "Differential Forms in Algebraic Topology" ISBN 0387906134

Evaluation: 100% assignments (5 assignments, 20% each.)

Assignment I (PDF) Due Sept. 21 during class. Selected solutions (PDF)

Assignment II (PDF) Due Oct 12, during class.

Assignment III (PDF) Due Nov 5, during class.

Assignment IV (PDF) Due Nov 19, during class. Selected solutions (PDF)

Assignment V (PDF) Due Dec 10, during class.

Course Overview: This is a first course in differential geometry. We will hope to cover the following topics.

• I Introduction to manifolds, vector fields, bundles, flows.
• II Differential forms and tensor fields
• III Integration and de Rham cohomology
• IV Morse theory
• V Hodge theory