Text: There will be no textbook for the course. My lecture notes will be posted on sakai. Below are some nice references:
- Marvin J. Greenberg, J. R. Harper, Algebraic Topology: A First course. Publisher: Westview Press.
- A. Hatcher: algebraic topology, Cambridge University Press.
- James W. Vick, Homology Theory: An Introduction to Algebraic Topology (Graduate Texts in Mathematics), Springer.
Prerequisites: Point set topology and advance calculus
This course will be an introduction to algebraic topology and basic manifold theory. The plan is to cover the following topics: fundamental group, Van Kampen's Theorem, covering spaces, simplicial and singular homology, cohomology, Brouwer's fixed-point theorem, and the Jordan-Brouwer separation theorem. We will emphasize on how to compute algebraic invariants by going over many interesting examples.