This one year course is aiming at preparation of studying global manifold
theory (especially low dimenison). In the first semester, We are going to
study the algebraic topology theory with the application to manifold
situation in mind.
1. Fundamental groups and covering space.
2. Homology groups and cohomology groups.
(including celluar theory, universal coefficient theorem
and Kunneth formula)
3. Poincare duality (also Lefshetz duality)
4. Short introduction of homotopy group
As for 2nd semenster, a tentative schdule is as follow:
5. De Rham cohomology (2nd )
6. Characteristic class
7. Spectral Sequence.