## 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).

Professor: Lorenzo Sadun, RLM
9.114, 471-7121,
sadun@math.utexas.edu

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.