Math 4432
  
Information
    

Professor: John Etnyre
Office: Skiles 106
Phone: 404.385.6760
e-mail: etnyre "at" math.gatech.edu

Office Hours: 1:00 - 2:00 on Thursdays.

Lectures: Thuesday-Thursday 3:05 - 4:25 in Skiles 246

Syllabus

The official syllabus for the class is at Math 4432 but a more details outline of the course is:

  • Intro to topology (topological spaces, basic topological properties, quotient spaces)
  • Intro to manifolds and statement of the classification of 1-manifolds and 2-manifolds
  • Intro to groups, with a focus on group presentations
  • The fundamental group of a topological space
    applications:
    • homeomorphisms of surfaces and the fundamental group,
    • free product decompositions of groups,
    • and other topics
  • The fundamental group and knot theory
  • Coverings spaces
    applications:
    • free groups,
    • Kurosh subgroup theorem,
    • and other topics
  • Homology
  • If time permits we will then see how to use all of this to study knots, 3-manifolds, exotic smooth structures on 4-manifolds, Khovanov homology, etc.

Textbook

There is no required text for this course. I will try to make the lectures fairly self-contained. However, there are many good textbooks on topology and algebraic topology. If you would like a text that will cover many of the things in this course I recommend:

  • Topology: a geometric approach by Terry Lawson.
  • Basic Topology by M.A. Armstrong.

Grading Policy

The course grade will be based on the following.

Homework: 50%
Midterm: 15% each
Term Paper: 20%

Homework Policy

Every week or two I will assign a set of homework problems. You should check the homework web page regularly, since I will not always announce when I post an assignment. You will have between one and two week to work on the problems (the exact due date will be on the problem set).

Exams

Midterm 1 is tentatively scheduled for Thursday, February 23
Midterm 2 is tentatively scheduled for Thursday, April 20

If you need to miss an exam talk to me in advance if possible, or if not then as soon after the exam as possible. We will arrange an alternate time for you to take a make-up exam.

Term Paper

Each student will write a term paper for the class. The paper will cover some topic in topology, algebra, algebraic topology, or its application to some other area (physics, biology, data analysis, etc.). The idea is for you to explore some area you find interesting related to the class.

The paper will need to have

  1. a significant mathematical component (that is proofs, computations, or the like) and
  2. have a good exposition (that is, written well enough to other students to learn something from the paper).

The target audience for these papers is other students. In fact part of the grade on the paper will be your providing helpful and constructive feedback to other students. Knowing who your audience is will help you while writing the paper and by seeing what others are doing well and not so well, you will be able to get a better idea how to be a better writer yourself.

Your grade on the paper will be determined by the following

  • 5% Consulting with me by the end of January on a topic for your paper
  • 15% Draft of your paper turned in by March 30
  • 20% Constructive feed back you provide on 2 other students papers (by April 11)
  • 60% Final paper turned in by April 25

When you turn in the draft of the paper, you will turn in three copies. I will then assign 2 other students to read your paper and provide feedback (there will be a feedback form to fill out for each paper you read). The feedback will be constructive and kind. (If you make negative comments that are un-helpful and un-constructive. Then I will not give the comments to the student and you will get a 0 for this 20% of the grade.) I will give you a form to fill out where you will answer a few questions about the paper and provide some short written feedback. I will collect the student feedback and my own and return it to you shortly after April 6. You can use this to make the final version of your paper to be turned in April 25.

The paper will need to be 4 to 8 pages (you can talk to me to get approval if you have a good reason for the paper to be shorter or longer) and be turned in as a pdf document. You should try to write the paper in TeX or LaTeX (ask me if you do not know about this), but I will accept any pdf document (so you can use Word or some other program to create the paper if you like). I will post the final versions of the paper on the T-Square site so other students can read them if they would like to do so.

Your paper can be on anything you like, but here are some thoughts to get you started.

Honor Code

All students must follow the GA Tech honor code.