This is an introductory course in algebraic topology. We will begin by covering the basics of homotopy theory, fundamental groups and classifying spaces. We then move on to CW-complexes and homology theory from various perspectives. Finally we will develop as much cohomology theory as possible before the end of the semester.

The only prerequisite for the course is a basic understanding of point set topology and group theory. Here are some basic notes on quotient spaces that might help refresh this important idea (we will be using this to "glue" spaces together all the time).

Lectures: Tuesday and Thursday 3:05 in Skiles 171.
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 six homework assignments.

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 four such problems) and turn them in to me in class on September 6. Please do try to work the other problems though. If you have any questions stop by my office.

• Read Hatcher pages 1-14 (through example 0.14).
• Chapter 0, problems 3, 5, 6, 18, 20
• Chapter 1.1, problems 5, 6, 7, 16, 20
• Chapter 1.2, problems 7, 9, 11, 14, 21
• Read through these applications of our computation of the fundamental group of S^1 (these notes were from a course I taught a while back so ignore the first half page of the notes).

Homework Assignment 2: Again you only need to turn in the underlined problems, but please try to work the others too. If you have any questions on these problems just stop by my office. This assignment is due on October 11.

• Chapter 1.3, problems 9, 10, 12, 15, 18, 29
• Read Section 1.A
• Chapter 1.A, problems 3, 8, 11
• Chapter 2.1, problems 13, 15, 20, 29

Homework Assignment 3: Again you only need ot turn in the underlined problems, but please try to work the others too. If you have any questions on these problems just stop by my office. This assigment is dues on November 6.

• Chapter 2.1, problems 17, 29
• Chapter 2.2, problems 9, 12, 21, 22,23, 27, 30, 32, 40

Homework Assignment 4: Again you only need ot turn in the underlined problems, but please try to work the others too. If you have any questions on these problems just stop by my office. This assigment is dues on December 4.

• Chapter 3.1: problems 5, 8, 9, 12
• Chapter 3.2: problems 1, 2, 11
• Chapter 3.3: problems 6, 7, 9, 10