Instructor
Shelly Harvey
Herman Brown 446
Phone: x3659
email: shevlly at rice.edu (take out v)

Course Information
Class meets: MWF 1pm -- 1:50pm in HB 423 (for 10 of the 15 weeks)
Credit hours: 2
Office Hours: TBA
Webpage: http://math.rice.edu/~shelly/543s10/
All homework and reading assignments can be found on Owlspace

Course Description
This will be an introductory course in 4-dimensional manifolds. 4-Manifolds are mysterious creatures; they don't quite act like low or high-dimensional manifolds. For example, in dimensions less than 4, each topological manifold admits exactly one smooth structure. In dimensions greater than 4, each topological manifold admits at most a finite number of smooth structures. However, in 4-dimensions, there are simply-connected closed 4-manifolds that admit infinitely many distinct smooth structures. In fact, to this day, there are no smooth 4-manifolds known to admit a finite number of smooth structures.

Some of the topics that will be covered:
  • Intersection forms of 4-manifolds
  • Classification of simply-connected 4-manifolds up to homotopy equivalence and homeomorphism
  • Characteristic classes of 4-manifolds
  • Examples of 4-manifolds: complex surfaces, blow-ups, Lefschetz pencils and fibrations, fiber sums
  • Kirby diagrams and Kirby calculus
  • Symplectic 4-manifolds and Stein surfaces

Resources
  • 4-Manifolds and Kirby Calculus by R. Gompf and A. Stipsicz (required textbook)
  • The Wild World of 4-Manifolds by A. Scorpan
  • The Topology of 4-manifolds by R. Kirby

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.