Differential Geometry (2016 Spring)

Room: 綜三723
Time: Monday n56 12:20-1:10, 1:20-2:10, 2:20-3:10

Course Description

We would like to introduce varies geometry and topology this semester. The material that we would like to cover in the course includes (but not limiting to) the following:

Laplace operator and Hodge theory, Poincare duality (Jost)
Fundamental group and covering spaces
Complex projective space, Kahler manifold
Symmetric spaces
Morse theory

Presentation

The students will read the following books and present what they learn in class. The purpose of this activity is to help the students developing the ability of independent study.

J. Milnor, Topology from the differential point of view
Y. Matsumoto, An introduction to Morse theory

References (待續)

Geometry:

I. Singer and J. Thorpe, Lecture notes on elementary topology and geometry (Chapter 3)
S. Kobayashi, Foundations of Differential Geometry I & II
J. Jost, Riemannian Geometry and Geometric analysis

Lie theory:

L. Duistermaat, Lie groups (1.1-1.4: Lie group and Lie algebra; 2.1-2.4: group actions and associate bundles)

Morse theory:

J. Jost, Riemannian Geometry and Geometric analysis (Chapter 7)
M.Audin and M. Damian, Morse theory and Floer homology (Appendix and Part I)
J. Milnor, Morse theory

Complex geometry:

D. Huybrechts, Complex Geometry

Syllabus

2/15: Laplace operator and Hodge star operator
2/22: Hodge theory and Poincare duality
2/29: National Holiday
3/7: Compactly supported cohomology (presentation: Chapter 1)
3/14: Compactly supported cohomology (presentation: Chapter 1)
3/21: Covering space and fundamental group (presentation: Chapter 2)
3/28: Covering space and fundamental group (presentation: Chapter 2, 3)
4/4: National Holiday

4/11: Covering space and fundamental group(presentation: Chapter 3, 4)
4/18: Seifert-van Kampen Theorem, Higher Homotopy groups(presentation: Chapter 4)
4/25: Higher Homotopy groups, varies geometry(presentation: Chapter 5)
5/2: move to 6/13
5/9: Symplectic geometry (presentation: Chapter 6)
5/16: (Almost) complex geometry (presentation: Chapter 6)
5/23: Complex geometry(presentation: Section 1.3)
5/30: Kahler geometry(presentation: Section 1.4)
6/6: Kahler geometry(presentation: Section 1.5)
6/13: Kahler geometry(presentation: Section 2.2)

Evaluation

In class presentations

Last Updated: May 16, 2016
URL: http://www.math.nthu.edu.tw/~nankuo/DG2016.html