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 SL2(Z): (pdf)
- Worksheet 2 (orientations of simplices): (pdf)
- Group actions: (pdf)
- Quaternion worksheet: (pdf)
Return to: Richard Hain *
Duke Mathematics Department *
Duke University