This is the main page for Math 382D (Differential Topology), unique number 54710.
I am Andy Neitzke; my office is RLM 9.134. My office hours are 4-5pm on Monday, or by appointment.
The teaching assistant is Richard Hughes; his office is RLM 10.146. His office hours are 11am-12pm on Wednesday.
This course meets MWF from 1:00-2:00pm, in RLM 11.176.
The main text will be Guillemin and Pollack, "Differential Topology"; you should have a copy. Another very nice book which I strongly encourage you to look at is Milnor, "Topology from the Differentiable Viewpoint." Finally, Frank Warner's "Foundations of Differentiable Manifolds and Lie Groups" would be a very useful extra resource.
There will be a midterm exam (take-home) and a final exam (at the standard scheduled time). Homework will also be graded. The letter grade for the course will be determined by: 25% homework (see below), 35% midterm, 40% final exam.
The core topics of the course are: smooth manifolds and maps, Sard's Theorem and transversality, intersection theory, differential forms and integration. Along the way we will cover various subtopics including Whitney embedding, fiber and vector bundles, tangent and cotangent bundles, orientations, Brouwer's fixed point theorem, degree of a smooth map, Borsuk-Ulam theorem, vector fields and flows, Poincare-Hopf theorem, Gauss-Bonnet theorem for hypersurfaces, de Rham cohomology, Lefschetz formula (this list may be adjusted a bit as the semester goes on.)
I will post my notes from the lectures below. The mapping between files and lectures is not 1-1. Notes will be updated to correct errors/omissions where they are helpfully pointed out or where I notice them later. I apologize for whatever errors remain.
I will post exercise sheets here. There will be one exercise sheet per week, due Friday in class, beginning with Friday Jan 30. The first exercise sheet (numbered 0) is not to be turned in; it contains some useful background material and preliminaries.
The University of Texas at Austin provides upon request appropriate academic accommodations for qualified students with disabilities. For more information, contact the Office of the Dean of Students at 471-6259, 471-4641 TTY.