MT 855: Surfaces, braids, and homology-type invariants
Time/Location: WF 3:00-4:15, Maloney 560
Instructor: Eli Grigsby
Office hours: Th 2-4, Maloney 522 or by appointment
Course description: I will discuss some 2-, 3-, and 4-dimensional aspects of braid theory from both an algebraic and topological point of view, emphasizing connections to contact/symplectic geometry. Along the way, I will introduce tools from Khovanov homology and Heegaard Floer homology that have proven to be quite useful in studying smoothly properly imbedded surfaces in the 4-ball (e.g.: the knot Floer complex as a (Z+Z)-filtered object, the tau invariant, the s invariant, and their younger cousins: Hom's epsilon invariant and Ozsvath-Stipsicz-Szabo's Upsilon invariant). We'll also probably spend a reasonable amount of time talking about the slice-ribbon conjecture, since you should all be working on it...once you get tenure. (J/K. Sort of.)
What follows is an incomplete list of books/articles to keep on your bedside table for reference.
Obviously, we will be able to recite each one by heart by end-of-semester.
Heegaard Floer homology:
Other useful (for me) background references:
- Glen Bredon, Topology and Geometry
- Robert Gompf and András Stipsicz, 4-manifolds and Kirby Calculus
- Victor Guillemin and Alan Pollack, Differential Topology
- Allen Hatcher, Algebraic Topology*
- Burak Ozbagci and András Stipsicz, Surgery on Contact 3-manifolds and Stein Surfaces*
*These may or may not be available in electronic form! E-mail me for assistance.