This is the first graduate class dedicated to algebraic topology. We will be covering all the basics of homology and cohomology theory and higher homotopy groups. If time permits we will cover some more advanced topics such as obstruction theory and/or spectral sequences.

The only prerequisite for the course is the Introduction to Geometry and Topology I (Math 6457) though having had Math 6458 would also be useful. I will be assuming you are familiar with the fundamental group and covering spaces. While prior exposure to homology/cohomology would be good, it is not necessary.

Announcements:

• The first class will be August 20 (I will be out of town on the 18th).

Lectures: Tuesday and Thursday 3:05 in Skiles 240.
Professor: John Etnyre
Office: Skiles 106
Phone: 404.385.6760
e-mail: etnyre "at" math .gatech.edu

Grading Policy

Grading for the class will be based on approximately four to six homework assignments and class attendance/participation.

The assignments will be posted below and will be due in class on the day indicated on the assignment.  I encourage you to work on these assignments with other students in the class and to use whatever other resources you might have, but each problem must be written up in your own words by you. At some point everyone needs to learn TeX or LaTeX so I encourage you to write up your homework using one of these packages, but this is not a requirement. If you would like help getting started with TeX or LaTeX you are welcome to talk to me about it.

Textbook

The textbook for this class is Algebraic Topology by Hatcher. The text is available on-line, but is is a fairly inexpensive book and having a hard copy can be a nice reference. There are many good textbooks for algebraic topology, but I just mention one other book you might find useful: Topology and Geometry by Bredon.

Homework

Homework Assignment 1: I have assigned many problems, but do not write up all of them. Carefully write up the underlined ones (there are just five such problems) and turn them in to me in class on September 22. Please do try to work the other problems though. If you have any questions stop by my office.

• Chapter 2.1, problems 11, 12, 14, 15, 17, 18, 29
• Chapter 2.2, problems 9, 12, 21, 22, 23, 30, 32

Homework Assignment 2: I have assigned many problems, but do not write up all of them. Carefully write up the underlined ones (there are just five such problems) and turn them in to me in class on October 27. Please do try to work the other problems though. If you have any questions stop by my office.

• Chapter 3.1, problems 4, 5, 8, 13
• Chapter 3.2, problems 1, 7, 8, 11
• Chapter 3.3, problems 7, 8, 10, 11, 24,

Homework Assignment 3: The assignment is here. Due in class on December 1.