Instructor
Shelly Harvey
Herman Brown 410
Phone: x3659
email: shevlly at rice.edu (take out v)

Course Information
Class meets: TR 10:50am -- 12:05pm in HB 427
Office Hours: TBA
Webpage: http://math.rice.edu/~shelly/542s09/
All homework and reading assignments can be found on Owlspace

Course Description
In recent years, we have seen an abundance of interesting new knot, link, and 3-manifold invariants that arise as the homology of a chain complex: Heegaard Floer homology, Chekanov-Eliashberg homology (aka legendrian contact homology), higher-order Alexander homology, and Khovanov homology. These innovations can be used to
  • determine the genus of a knot and the Thurston norm of a 3-manifold,
  • determine whether a knot is fibered,
  • detect whether a knot is the unknot,
  • find transverse/legendrian knots that have the same classical invariants but which are distinct up to transverse/transverse isotopy,
  • detect whether a knot is slice, and
  • give a purely combinatorial proof of the Milnor conjecture.
This course will serve as an introduction to the first three homology theories listed above and their applications. If time permits, we will also outline the construction and applications of Khovanov homology as well as its relationship to Heegaard Floer homology.

Resources
Heegaard Floer Homology
  • Introduction to Heegaard Floer Homology by Peter Oszváth and Zoltan Szabó - Lecture notes from the first lecture course on Heegaard Floer homology taught by Z. Szabó during the Clay Mathematics Institute Budapest Summer School in June 2004.
  • Lectures on Heegaard Floer homology by Peter Oszváth and Zoltan Szabó - Lecture notes from the second lecture course on Heegaard Floer homology taught by P. Oszváth during the Clay Mathematics Institute Budapest Summer School in June 2004.
  • Heegaard diagrams and holomorphic disks by Peter Oszváth and Zoltan Szabó - A survey paper on Heegaard Floer Homology
Chekanov-Eliashberg Homology Higher-order Alexander homology Khovanov Homology

Grades
Your grade in the class will be based on homework, attendance, and class participation.

Homework
Homeworks will be posted on OWL-Space (use your netid to log in). You will receive an email from OWL-space as soon as the homework is posted. Homework solutions must be legible.

Disability Support
Any student with a documented disability needing academic adjustments or accommodations is requested to speak with me during the first week of class. All discussions will remain confidential. Students with disabilities need to also contact Disability Support Services in the Ley Student Center.