:: Knot concordance and homology cobordism ::

Math 8803: Knot concordance and homology cobordism

Email: hom [at] math.gatech.edu
Location: Swann 325
Time: Mondays and Wednesdays 9:30-10:45 am
Office: Skiles 208B
Office hours: Mondays and Wednesdays 10:45-11:45 am and by appointment

We will study knot concordance and homology cobordism. We will discuss both classical and modern tools for studying these objects, as well as their relationship to topics such as exotic structures on smooth 4-manifolds and triangulations of high dimensional topological manifolds.

Prerequisites

Math 6441 (Algebraic Topology) or consent of instructor

Assignments

Your grade will be based on classroom participation and assignments. At times throughout the lectures, I will leave parts of some proofs as exercises. There are also related exercises in some of the references below. At the end of each month (January, February, March, and April), you will turn in 5 exercises, which will be graded for completion. An assigment will be considered complete if most of the exercises are completed correctly (i.e., you have correctly conveyed the main idea, although there may be some minor errors in the details). For any exercises that you were unable to complete, you should describe what you tried, why it didn't work, what you tried next, and what you are still confused about.

Alternatively, instead of turning in 5 exercises, you may give a talk in the Wednesday student geometry-topology seminar.

Resources

The following references may be helpful:

R. Gompf and A. Stipsicz, 4-manifolds and Kirby calculus
J. Hom, Homology cobordism, knot concordance, and Heegaard Floer homology
C. Livingston, A survey of classical knot concordance
C. Manolescu, Lectures on the triangulation conjecture
D. Rolfsen, Knots and links
N. Saveliev, Lectures on the topology of 3-manifolds

Class Notes

Will be posted here.
Notes thanks to Sierra Knavel. All errors are my own.

Additional Information