## Math 611, Algebraic Topology

## Fall 2022

**Instructor:** Richard Hain
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

There will be lots of examples and applications to help students learn the
material.
**Text:** Hatcher, Allen: *Algebraic
topology*, Cambridge University Press, Cambridge, 2002.

**References:**
- Greenberg, Marvin J:
*Lectures on algebraic topology*, W. A.
Benjamin, Inc., New York-Amsterdam 1967. (Out of print.)
- Hatcher, Allen:
*Algebraic
topology*, Cambridge University Press, Cambridge, 2002.
- Munkres, James:
*Topology*, 2nd edition, Prentice Hall, 2000.
- Munkres, James:
*Elements of Algebraic Topology*, Perseus,
1984.
- 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
*SL*_{2}(Z): (pdf)
- Worksheet 2 (orientations of simplices): (pdf)
- Group actions: (pdf)
- Quaternion worksheet: (pdf)

Return to: Richard Hain *
Duke Mathematics Department *
Duke University