Geometric Topology (MAS 480 25.480)

Monday, Wednesday, Friday:14:00-15:00 Room: E6 2412

Instructor: Suhyoung Choi Room: E6-4403

e-mail: shchoixk at math kaist ac kr

Course Homepage: mathsci.kaist.ac.kr/~schoi/teaching.html

The basic purpose of this course is to study the geometric structures on orbifolds including hyperbolic geometry and discrete groups.
The level will be adjusted for beginning MA students.  We will cover my notes and relevant parts of (Ra) that are needed. We will use
Computer Algebra Systems such as mathematica, maple, or maxima.
(If you wish to enter into this area of mathematics, this will be a beginning course.)

Text books:
(Ch) S. Choi, Geometric structures on 2-orbifolds: exploration of discrete symmetry,
Preliminary version. Nov. 2009. (This is a temporary note from my Titech course taught
in the Fall of 2008. There are many references in here as well. Please download the file.)
(Th) Thurston, Three-dimensional geometry and topology, Princeton
(Ra) Ratcliffe, Foundations of hyperbolic manifolds, Springer
(He) Hempel, 3-manifolds, AMS

Other helpful references are:
(Br) Bridson, Haefliger, Metric spaces of non-positive curvature, Springer
(N) Walter Neumann, Notes on Geometry and 3-Manifolds, available from http://www.math.columbia.edu/~neumann/preprints/

There will be four reports (80% of the grade). We will take attendance seriously (20% of the grade).
Some report will be done by turning in computer graphics using mathematica or maple.

Schedule:

2/7-2/11: Chapter 2. Manifolds and differentiable structures.  Note 1
2/14-2/18: Chapter 2.
2/21-2/25: Chapter 3. Lie groups and geometry (from Ratcliffe also.) Note 2
2/28-3/4: Chapter 3.
3/7-3/11: Chapter 3.
3/14-3/18: Chapter 4. Topology of orbifolds Note 3-1
3/21-3/25 Chapter 4. Note 3-2
3/28-4/1: Midterm
4/4-4/8: Chapter 4.
4/11-4/15: Chapter 5. Topology of 2-orbifolds Note 4
4/18-4/22: Chapter 5.
4/25-4/29: Chapter 6. Geometry of 2-orbifolds
5/2-5/6: Chapter 6., Chapter 7. Deformation spaces of hyperbolic structures on 2-orbifolds
5/9-5/13: Chapter 7.
5/16-5/20: Chapter 8. (note not written yet)
5/23-5/27: Final

Final Report: You need to select a report you wish to make and give a plan to finish this to me by May 6th (2 pm).
You need to get an approval from me. This could be a program (available from web) or a mathematica file you wrote with
a report on it. The final due date for the report is May 23rd (2 pm). Please make an effort.