Fall 2008 Geometric structures on 2-orbifolds(Tokyo Institute of Technology)

Fall 2008 Geometric structures on 2-orbifolds
(Tokyo Institute of Technology)

 

 

Time: T 7-8
ROOM:

Instructor: Suhyoung Choi (visitor)
schoi at math dot kaist dot ac dot kr

This course will introduce 2-orbifolds and geometric structures on them. It will be for senior or master level course.
Some background in topology, manifold theory, differential geometry would be helpful.

Purpose: We will learn 2-dimensional orbifold theory and the geometric structures on them. We will cover
some of the background materials such as Lie group theory, principal bundles and connections.
The theory of orbifolds has much to do with discrete subgroups of Lie groups but has more topological flavors.
We discuss the topology of 2-orbifolds including covering spaces and orbifold-fundamental groups. The fundamental groups
of 2-orbifolds include many interesting infinite groups. Finally, we obtain the understanding of the deformation space
of hyperbolic structures on a 2-orbifold, which is the space of discrete representations of the 2-orbifold fundamental group
equivalent up to conjugations.

 

Lectures: (Please download the pdf files to be posted before the classes)

Dates	Content
10/ 7	Manifolds and differentiable structures
10/14	Manifolds and differentiable structures
10/21	Lie groups and geometry
10/28	Lie groups and geometry
11/4	Topology of 2-orbifolds: compact group actions
11/11	Topology of 2-orbifolds
11/18	Universal covers of 2-orbifolds
11/25	Topological constructions of 2-orbifolds
12/2	Geometric structures on 2-orbifolds
12/9	Constructions of geometric 2-orbifolds
12/16	Constructions of geometric 2-orbifolds
1/13	Deformation spaces of geometric structures on 2-orbifolds
1/20	Deformation spaces of hyperbolic structures on 2-orbifolds
1/27	Deformation spaces of real projective structures on 2-orbifolds

Note; I might change the content and schedule slightly as we progress.

 

Homework: They will be in the pdf files. 3-4 times.

 

Grades will be based on the homework.

 

I will try provide more details later.