Math 821 (Algebraic Topology)
Spring 2014

General Information | Textbook | Problem Sets | Lecture Notes | Links

General Information

Instructor: Jeremy Martin
623 Snow Hall, 864-7114
The best way to contact me is by e-mail:

KU course number: 65729
Meeting times: MWF, 1:00-1:50 PM, 564 Snow
Office hours: Mon 2-3, Wed 11-12, or by appointment (which I'm happy to make)

Prerequisites: Math 790-791 and 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. If you have taken additional algebra (e.g., Math 830), that will be helpful.
Final exam: Wednesday 5/14, 10:30-1:00.


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 from the publisher (list price $44).

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. Chapters 4-7 will not be necessary, but any familiarity with chapter 8 is a plus.
  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 are due in class every two weeks. I will post problems on the website at least a week in advance. Problem sets are subject to change before that time, so make sure you have the final version.

Number Due date Problems Q&A Solutions Figures, etc.
1 Fri 1/31 hw1.tex | hw1.pdf Q&A hw1-solns.tex | hw1-solns.pdf
2 Fri 2/14 hw2.tex | hw2.pdf Q&A hw2-solns.tex | hw2-solns.pdf
3 Fri 2/28 hw3.tex | hw3.pdf Q&A hw3-solns.tex | hw3-solns.pdf
4 Fri 3/14 hw4.tex | hw4.pdf Q&A hw4-solns.tex | hw4-solns.pdf dunce.pdf | torus-decomp.pdf
5 Fri 4/4 hw5.tex | hw5.pdf Q&A hw5-solns.tex | hw5-solns.pdf Macaulay2.tex | Macaulay2.pdf
6 Fri 4/18 hw6.tex | hw6.pdf Q&A hw6-solns.tex | hw6-solns.pdf Figure for #4 (Hatcher, p.132; I think this qualifies as fair use)
7 Fri 5/2 hw7.tex | hw7.pdf Q&A hw7-solns.tex | hw7-solns.pdf Figure for #1b | Figure for #1c | Figure for #3 |

Lecture Notes

Here are my lecture notes. They are password-protected (same username and password as for the solution sets) and are not for distribution.





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Last updated Thu 5/8/14