Math 821 (Algebraic Topology)
Spring 2011

General Information | Textbook | Problem Sets | Links

General Information

Instructor: Jeremy Martin

623 Snow, 864-7114

KU course number: 69608

Syllabus

Meeting times: MWF, 1:00-1:50 PM, 456 Snow (note change)

Office hours: Tuesdays 1:00-2:00, Wednesdays 2:00-3:00, or by appointment

Discussion group on Google (requires membership)

Prerequisites: Officially, "Math 820 or permission of instructor." Not all of the material covered in Math 820 will be necessary for Math 821, but you should know what a topological space is and what "continuous", "connected", and "compact" mean outside the context of metric spaces. You should also be comfortable working with vector spaces and groups --- i.e., you should have taken or be taking Math 790/791, and preferably Math 830 as well.

Textbook

The main textbook is Algebraic Topology by Allen Hatcher (Cambridge U. Press, 2002). The book is available as a free download from the author's website. If you choose to use the downloaded version, do not print out a copy on the department printer! You can also buy a paperback copy (e.g., from Cambridge U. Press or Amazon) for roughly $30.

Other books that may be helpful:

  1. J. Munkres, Topology: A First Course (a.k.a. "the red book") (Prentice-Hall, 1975). An excellent reference for basic topology. If you are comfortable with the material in the first three chapters of Munkres and you know some algebra, then you should be ready to take Math 821.
  2. G. Bredon, Topology and Geometry (Springer, 1993; reprinted 1997). I don't know this book well first-hand, but it has a good reputation. The topics covered and level of exposition are comparable to Hatcher's book.
  3. J. Munkres, Elements of Algebraic Topology (Addison-Wesley, 1984). Again, I don't know this book well first-hand, but Munkres' basic book is so good that this one probably is too.
  4. W. Massey, Algebraic Topology: An Introduction (Springer, 1977). A standard book with a focus on covering spaces and the fundamental group; does not discuss homology.
  5. M.J. Greenberg and J.R. Harper, Algebraic Topology: A First Course (Benjamin/Cummings, 1981). A standard textbook with a fairly abstract, algebraic treatment.
  6. E. Spanier, Algebraic Topology (Springer, 1966; reprinted 1981). Ditto.

Problem Sets

Problem sets will be posted on Fridays, starting 1/28/11, and will be due on the following second Monday (i.e., ten days later) at 5:00 PM. You must submit typed solutions, preferably using LaTeX. Hand-drawn figures are acceptable. You can either submit hard copies or send me the PDF version by e-mail.

# Assigned date Due date LaTeX sourcePDF documentFigures (if any)
1 Fri 1/28/11 Mon 2/7/11 hw1.tex hw1.pdf
2 Fri 2/11/11 Mon 2/21/11 hw2.tex hw2.pdf
3 Fri 2/25/11 Mon 3/7/11 hw3.tex hw3.pdf rotategraph.eps
4 Fri 3/11/11 Mon 3/28/11 hw4.tex hw4.pdf dunce.eps | torus-decomp.eps
5 Fri 4/1/11 Wed 4/13/11 hw5.tex hw5.pdf
6 Fri 4/15/11 Wed 4/27/11 hw6.tex hw6.pdf
7 Fri 4/29/11 Wed 5/11/11 hw7.tex hw7.pdf

LaTeX resources:

Links

Mathematical and technical writing information:

KU links:

Software:


Last updated Fri 4/29/11 4:00 PM CST