Program
Introduction to low dimensional geometry and topology
Student No.:50
Time:Tue/Thu 10:10-12:00, 2014-05-20 ~ 2014-08-28 (For classes on May 22/29 and June 5/12, time: 13:00-14:50; No classes on July 1/3, Aug 5/7/21)
Instructor:Feng Luo  [Rutgers University]
Place:Conference Room 4, Floor 2, jin Chun Yuan West Building
Starting Date:2014-5-20
Ending Date:2014-8-28

 

 

 

Description:
 
This course is intended for advanced undergraduate students and beginning graduate students who are interested in topology and geometry. It will be a combination of lectures, informal discussions and talks by students.
The main focus will be on topology and geometry in dimensions 2 and 3. We will begin with topological classification of surfaces and basic knot theory and move to Riemann surfaces, Teichmuller spaces, hyperbolic 3-manifolds and geometry of convex polytopes. Some of the basic material like fundamental groups will be introduced as well. If time permits, we will also go over some of the recent work on quantum invariants of 3-manifolds.
 

Prerequisite:

 
undergraduate algebraic topology (fundamental groups) and Riemann geometry (Riemannian metrics)
 

Reference:

1. Algebraic topology: books by Greenberg-Harper Greenberg, Hatcher and Vick.

2. Riemannian geometry: book by Do Carmo

3. Hyperbolic geometry and Teichmuller theory: book by Benedetti-Petronio, Foster

4. Knot theory: books by Rolfsen and Lickorish Convex polytopes: book by Alexandrov and Gruber