Math 611, Algebraic Topology

Fall 2022

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

Text: Hatcher, Allen: Algebraic topology, Cambridge University Press, Cambridge, 2002.

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 in 2006.

Assignments:

• Assignment 1: due 9/13 (pdf)
• Assignment 2: due 10/13 (pdf)
• Assignment 3: due 10/20 (pdf)
• Assignment 4: due 11/14 (pdf)
• Assignment 5: due 12/01 (pdf)
• Assignment 6: due 12/17 (pdf)

Handouts:

• Topology summary: (pdf)
• Spheres as quotients: (pdf)
• Products of quotient maps: (pdf)
• Worksheet 1 (knots and braids): (pdf)
• Old problem set on SL₂(Z): (pdf)
• Worksheet 2 (orientations of simplices): (pdf)
• Group actions: (pdf)
• Quaternion worksheet: (pdf)