Algebraic Topology, MATH 547, Spring 2010

Instructor: Daniel Groves, 538 SEO e.mail

Course webpage: http://www.math.uic.edu/~groves/teaching/2009-10/547/

Course hours:

MWF, 11:00-11:50AM, Room 311, Addams Hall.

Discussion Section:

Wednesday, January 27, 4pm, SEO 512.

Mondays at 4pm, SEO 512 (starting February 1, at least until midterm).

Office hours:

Monday 1:00-1:50pm, Wednesday 1:00-1:50pm, SEO 538. (You can also make an apointment by e.mail or try stopping past my office.)

Text: "Algebraic Topology" by Allen Hatcher.
This book is available for downloading here (or you can buy a bound copy for not very much money at all).

Course description:
The plan is to cover most of the material in Chapters 1,2 and 3 of Hatcher. (With some time at the beginning spent on preliminary material such as Chapter 0.)
This may prove to be too ambitious, in which case the plan will be revised along the way. Prerequisite knowledge for this class are some point-set topology (the quotient space construction is extremely important), and some abstract algebra (groups, rings, modules). I won't expect you to know any homological algebra. If you've taken Differentiable Manifolds I, then you'll have lots of examples under your belt, but it shouldn't harm your chances much if you haven't taken it.

Assessment: Homework sets will be due approximately every two weeks, starting Monday January 25). (In weeks when homework is not due, exercises will be set that you should attempt. Of course, in an ideal world you would do all of the exercises in Hatcher...) There will be one take-home midterm exam, and one take-home final exam. The relative weightings of these items will be discussed in class.

Homework sets:
  • Week 1 (not for turning in): Hatcher, Chapter 0, pp.18-20: #3, #9, #13, #14, #15, #16, #23, #27.

  • Week 2, Due: January 25 at the beginning of class. Hatcher, Chapter 1.1, pp.38-40: #1, #2, #5, #10, #12.

  • Week 3 (not for turning in): Hatcher, Chapter 1.3, pp.79-80: #4, #6, #9, #20, #23.

  • Week 4, Due: February 8 at the beginning of class. Hatcher, Chapter 0, pp.18-20: #17, #18, #24. Chapter 1.3, pp.80-81: #12, #17.

  • Week 5 (not for turning in): Hatcher, Chapter 1.1, pp.39-40: #17, #20. Chapter 1.2, pp.52-54: #2, #9, #10, #14.

  • Week 6, Due: February 22 at the beginning of class. Hatcher, Chapter 1.2, pp.53-54: #8, #11, Chapter 2.1, p.131: #4, #5, #7.

  • Week 7 (not for turning in): Hatcher, Chapter 2.1, pp.131-132: #2, #8, #11, #12, #13

  • Week 8, Due: March 8 at the beginning of class. Hatcher, Chapter 2.1, pp.132-133: #15, #16, #17, #18, #22.

  • Week 9 (not for turning in): Hatcher, Chapter 2.1, p.133: #23, #26, #27, #29, Chapter 2.2, p.155: #1, #2, #3.

  • Week 10: No HW.

  • Week 11, Due, April 5 at the beginning of class. Hatcher, Chapter 3.1, pp.205-206: #2, #5, #6, #9, #12.

  • Week 12 (not for turning in): Hatcher, Chapter 3.1, p.205: #1, #4, #8, #11.

  • Week 13, Due April 19 at the beginning of class. Hatcher, Chapter 3.2, pp.228-229: #1, #3, #6, #7.

  • Week 14, No homework.

  • Take home final: Due Monday, May 3, 11am. Hatcher, Chapter 1.1, p.39: #16. Chapter 1.3, p.80: #14. Chapter 2.1, p.133: #28. Chapter 2.2, p.156: #9. Chapter 3.2, p.229: #9.

    This final will be worth 40% of the final grade. No collaboration is allowed.