Math 261, Algebraic Topology

Spring 2010

This will be a standard 1-semester course in algebraic topology. Topics to be covered include:

• cutting and pasting
• the fundamental group
• covering spaces
• singular homology and its basic properties
• simplicial and cellular homology
• Euler characteristic

I have not yet decided on a text. References:

1. Greenberg, Marvin J: Lectures on algebraic topology, W. A. Benjamin, Inc., New York-Amsterdam 1967. (Out of print.)
2. Hatcher, Allen: Algebraic topology, Cambridge University Press, Cambridge, 2002.
3. Munkres, James: Topology, 2nd edition, Prentice Hall, 2000.
4. Munkres, James: Elements of Algebraic Topology, Perseus, 1984.
5. Spanier, Edwin H: Algebraic topology, Corrected reprint. Springer-Verlag, New York-Berlin, 1981. (This is a standard reference.)

Quote: "A topologist is somebody who does not know the difference between a bagel and a coffee cup." Colbert on donuts and spheres.