Graduate Algebraic Topology


Unique number: 56350

Meeting time and place: MWF 9-10, RLM 9.166

Instructor: Lorenzo Sadun, RLM 9.114, x1-7121

Web site: http://www.ma.utexas.edu/users/sadun/F01/382C/

Office hours: Tu-Th 9-11

Textbook: A Basic Course in Algebraic Topology by William Massey. We will cover most of chapters 1-9, and maybe a little of chapter 12 (cohomology) if there is time.

Prerequisites: You need to know undergraduate topology pretty well. On the algebraic side, you need to know what a group is, and to be able to do basic group operations, like taking the quotient of a group by a normal subgroup. That's pretty much it.

Tests: There will be two exams, tentatively scheduled for Friday, October 12 and Friday, December 7 (the last day of class). If you have any unavoidable conflicts with these dates, please see me as soon as possible. The exams, especially the final, will be modeled on the prelim itself, with several difficult problems to choose from.

Homework: Problem sets will be due every week, on a day of the week that will be decided at the first class meeting.

Term paper: Part of your assignment it to write a paper on some interesting aspect of topology that isn't covered in class. You can give an alternate proof of an interesting theorem, or an interesting application, or prove an interesting theorem that we just didn't reach this term. The key word is ``interesting''. Find something interesting to say about topology, and say it!

You are encouraged to work together, both on homework and on the term paper. (Up to four names may appear on one termpaper). I especially encourage you to work with somebody at a similar level of understanding as yourself, so it isn't one person carrying another along. By talking things over, you'll both learn more. Of course, your homework papers should in the end reflect your own understanding and work, but collaboration is a very good way to achieve that understanding. [For what it's worth, all but 5 of my journal articles to date have been collaborations.]

Grading: The midterm will count 25%, the final will count 35%, while homework and the term paper will each count 20%. Qualitatively, here's my grading scale: An ``A'' means that I think you're ready to pass the (first half of the) topology prelim exam. A ``B'' means that you learned a fair amount but are not yet ready for the prelim exam. The grade of ``C'' is reserved for those who don't take the course seriously, as evidenced by repeatedly skipping homework, writing a junky termpaper, and/or bombing the exams.

Disabilities: As all of you who are TAs know, ``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.''