Math 821 (Algebraic Topology)
Spring 2014

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

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

KU course number: 65729
Syllabus
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 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.

• You are encouraged to collaborate with other students, but you must write up the problems by yourself and acknowledge all collaborators. You should not consult outside sources such as the Internet.
• You must submit typed solutions using (La)TeX (it is OK to draw figures by hand). Here is a header file with common macros; the TeX files below require that header.
• Late homework will not be accepted.
• The username and password to access the solution sets are respectively the first and second words in the title of the course (all lower-case).
• See the page of questions and answers about the problem sets (last updated 4/30/14).

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

• Hatcher Chapter 0
• Hatcher Chapter 1
  • Excerpt: Proof of Van Kampen's Theorem (2/24/14)
• Hatcher Chapter 2 (5/7/14)

Topology

• Simplicial complexes and Delta-complexes (J.M. Boardman)

Software

• Macaulay2 (free commutative algebra software)
• Macaulay2 web server
• Getting Started with M2 (my handout)
• Sage (free, open-source, general-purpose mathematical software)

LaTeX

• Header file for .tex files on this website; feel free to use it when writing up problem sets
• KU Math Department LaTeX page (includes getting-started links and information about TeXMaker and TeXShop workspaces)
• TeX resources from the American Mathematical Society
• LaTeX symbols (short list, contains most standard symbols)
• The Comprehensive LaTeX Symbol List (extremely long list; probably more symbols than anyone would ever need!)
• DeTeXify (optical recognizer for LaTeX symbols)
• xypic, a package for typesetting commutative diagrams. See in particular the user's guide.
• Ipe (package for creating figures; recommended by several students)

Mathematical and technical writing guides

• A Guide to Writing Mathematics
• A Guide to Writing in Mathematics Classes
• A Mathematical Writing Checklist

KU links

• Jeremy's home page
• Mathematics Department
• Registrar
• Academic misconduct policies
• Student Access Services (for students with disabilities)