This course will cover advanced topics in Algebraic Topology. We will cover homotopy theory, including H and H’-spaces, homotopy groups, and the Whitehead and Hurewicz theorems; and bundle theory, including principal bundles, classifying spaces, obstruction theory, and classifying spaces. If time permits, we might consider spectral sequences, cohomology operations, and other topics.

The prerequisites for the course are Algebraic Topology I. Specifically, I will be assuming you are familiar with fundamental groups, covering space , homology and cohomology. Though topics beyond thebasics will be reviewed.

You can find the class notes here.

Lectures: Monday-Wednesday 9:30-10:45 in Skiles 154.
Professor: John Etnyre
Office: Skiles 106
Office Hours: 10:00-10:55 Fridays (also feel free to set up an appointment via e-mail).
Phone: 404.894.6614
e-mail: etnyre "at" math .gatech.edu

In person and online content: COVID precautions

Classes will be in person. I will record classes so that people can watch them if they are unable to attend class for some reason. I am also posting class notes that can be used to keep up with the class if you cannot attend all the classes in person. The recordings are not great, but hopefully together with class notes, one can make up a missed class. It is highly recommended that you try to addend in person as much as possible, the live interaction with the easy ability to ask questions is very helpful in learning the material. 

Our classroom should have enough seating to allow people to be somewhat distanced from one another and I encourage you to keep as much distance as possible from each other. Also, please use the same seats each day in class. This will help with contact tracking should someone come down with COVID. 

All of these policies are subject to change as guidance for the CDC and Georgia Tech change.

Grading Policy

Your grade will be based on class participation and some class assignments. For the class assignments, in the each of the months of September, October, and November, by the end of the month you need to either turn in 4 problems mentioned in class or in one of the text books (related to the material being covered in class) or alternatively give a talk in the Wednesday student geometry/topology seminar that month. The written assignments must be turned in by the end of month. The assignments will be graded on a pass/fail basis. A reasonable attempt will receive a pass. By reasonable attempt, I mean that the attempts for solutions to 3 out of 4 of the problems essentially correct even if there might be some minor errors. If you give a talk, that will count as a completed assignments for that month.

For solving the written problems you are welcome to consult with me or work with other students. But the problems must be written up by you, in your own words.

To receive passing grade you must complete and pass the monthly assignments. For an A you must also attend at least 90% of the classes (or have an excused absence), for an B you must attend at least 80% of the classes (or have an excused absence), for a C, 70%, and for a D, 60%. Due to the pandemic, I realize that some people might have difficulty participating in class as much as they would like (and to meet the cut-offs for the given grades). If you need to miss classes (maybe even all!), please just contact me and explain the situation and verify that you are keeping up with the class (thought recordings and class notes published on the website).

Textbook

There are no official text book for this course, but the following books are are some of my favorite books on the subject (and cover much more!):

• Homotopical Topology
  by Anatoly Fomenko, Dmitry Fuchs
• Lecture Notes in Algebraic Topology
  James F. Davis and Paul Kirk
• Rational Homotopy Theory and Differential Forms
  Phillip Griffiths, John Morgan
• Vector Bundles and K-Theory
  by Allen Hatcher

These books might be available through the GT library or legally online.

Miscellaneous matters

• Academic Integrity. All students are expected to comply with the Georgia Tech Honor Code.
• Students with Disabilities and/or in need of Special Accommodations. Georgia Tech complies with the regulations of the Americans with Disabilities Act of 1990 and offers accommodations to students with disabilities. If you are in need of classroom or testing accommodations, please make an appointment with the ADAPTS office to discuss the appropriate procedures.
• Intent for Inclusivity. As a member of the Georgia Tech community, I am committed to creating a learning environment in which all of my students feel safe and included.  Because we are individuals with varying needs, I am reliant on your feedback to achieve this goal.  To that end, I invite you to enter into dialogue with me about the things I can stop, start, and continue doing to make my classroom an environment in which every student feels valued and can engage actively in our learning community.