## M382D Differential Topology

Unique #: 55670

Meeting time and place: ETC 2.102 (NOT RLM 11.167.  I had to get a new room, with projection, to accomodate my injured arm).

TA: Jason Deblois, RLM 10.110, 5-9143, jdeblois@math.utexas.edu

Office Hours: Tentatively MW10-11

Textbook: Differential Topology, by Guillemin and Pollack.  Another useful reference, both for the underlying calculus and for differential forms, is Spivak's Calculus on Manifolds.  There will be roughly 2 weeks of preliminary material at the beginning of the term that is not in the text.

Homework: There will  be weekly problem sets, due on Fridays.

Collaboration: You are encouraged to work together on homework, and to explain your solutions to one another before turning them in.  The best way to tell whether you really know something is to try to explain it to somebody else. However, the written solution you eventually turn in should reflect your own personal understanding.  (Learning from one another is great -- giving each other free rides is self-destructive).

Exams:  There will be two midterms, on the day before Spring Break and the last day of class.  I will try to make these midterms resemble prelim exams, albeit shorter.

Term paper: You are expected to write a term paper, either alone or in collaboration with others.  Pick a theorem of differential topology and discuss it.  You can explain its history, the ideas behind it, applications of it, different approaches to it, an elementary way of viewing it, or whatever you like.  The paper should be between 3+n and 4+2n pages, where n is the number of people in the collaboration. Your topic should be chosen by spring break, and the paper is due one week before the end of classes.

Grading: Your grade will be based 30% on homework, 20% on the term paper, 20% on each midterm, and 10% on my subjective evaluation of your  performance.

Syllabus:  We will cover all of Guillemin and Pollack, in slightly more generality than the text, since we will consider abstract manifolds, not just manifolds embedded in R^n.   See the course schedule.