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

Time: T 7-8
ROOM:

Instructor: Suhyoung Choi (visitor)
schoixk at gmail dot com

Course homepage: http://www.is.titech.ac.jp/~schoi/dgorb.htmor math.kaist.ac.kr /~schoi/dgorb.htm

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.

We will write a book based on this course to be submitted to be a part of
Mathematical Society of Japan Memoirs, a series published by World Scientific Co.

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

Dates	Content
10/ 7	Manifolds and differentiable structures	Handout 1
10/14	Manifolds and differentiable structures
10/21	Lie groups and geometry	Handout2
10/28	Lie groups and geometry	Handout2p2.
11/4	Topology of 2-orbifolds: compact group actions	Handout3
11/11	Topology of 2-orbifolds	Handout4
11/18	Universal covers of 2-orbifolds	Handout5
11/25	Topological constructions of 2-orbifolds	Handout6
12/2	Geometric structures on 2-orbifolds	Handout6p2
12/9	Constructions of geometric 2-orbifolds	Handout6p3
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	Handout7
1/27	Deformation spaces of real projective structures on 2-orbifolds

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

Final report. (Due Feb. 16^th with preliminary approval date January 9^th )

The final grade will be based on the final report.

Some examples of a real projective 2-orbifold

My talk at Titech related to this course

Two papers related to this course.

Geometric Structures on Orbifolds and Holonomy Representations (http://www.springerlink.com/content/g88n7t716t66712n/),

The deformation spaces of convex RP 2 -structures on 2-orbifolds (with Goldman) (http://muse.jhu.edu/login?uri=/journals/american_journal_of_mathematics/v127/127.5choi.pdf )