**Course outline:** Homotopy, fundamental group,
Van Kampen's theorem, fundamental theorem of algebra,
Jordan curve theorem, singular homology, homotopy invariance,
long exact sequence of a pair, excision, Mayer-Vietoris sequence,
Brouwer fixed point theorem, Jordan-Brouwer separation theorem,
invariance of domain, Euler characteristic, cell complexes,
projective spaces, Poincaré theorem.

**Instructor:**Dan Christensen**E-mail:**`jdc@uwo.ca`

**Office:**Middlesex 103b.**Office Phone:**519 661-2111 x86530.**Office Hours:**Fridays after class or by appointment.**Class times and location:**MWF 9:30-10:20 in MC108.**Prerequisites:**Group Theory (Math 3120) and General Topology (Math 3132 or Math 4121). Students are responsible for verifying that they have the correct prerequisites; please contact me if unsure.**Web page:**This page is available at http://jdc.math.uwo.ca/M9052, where you should also check for course announcements.

**Text:** The text for the course is
*Algebraic Topology*, by Allen Hatcher.
Published by Cambridge University Press.
ISBN 0-521-79540-0.
The seventh printing, from 2006, contains many corrections
and improvements.
The book will be available at the campus bookstore, and is
also available
online.
The book's webpage also contains a list of errata for the printed copy.

We will cover parts of chapters 0, 1 and 2. The textbook is a valuable resource that gives more examples and details than can be given during lecture. Students are expected to read the text book, going over what we have covered, reading ahead to what comes next, and studying additional examples.

Here is a list of other reading material. None of these are required, but you might find them interesting. Most of these are available in the library. I haven't put them on reserve, so share with other students.

**Homework:** Homework will be due every two weeks,
in class. Doing problems and talking about the
material are both essential for learning the material in this course,
so you are encouraged to **discuss**
the problems with classmates and with me.
But you must write up the solutions **on your own** and must not
look at other students' written solutions nor should you attempt to
find solutions to problems online or in textbooks.
Your solutions should be **clear** and **carefully written** and
you should give **credit** to
those who helped you and to any references you used.
Homework will be graded based on both correctness and clarity.
Late problem sets will not be accepted unless arranged in advance
for a good reason.

**Copying solutions** from other students, online sources,
textbooks, etc. or showing your work to other students
constitutes a scholastic offense and will result
in a grade of **-100%** for the assignment and in some cases
expulsion from the program.
All academic offenses are added to your student record.

**Presentations:** In the second half of the semester,
each student will give a presentation on a topic related to the
course. The scheduling will be worked out later.
See the presentations page for more details.

**Exam:** There will be a final exam
on Friday, December 16 at 1:30 pm in MC108.

**Evaluation:** Evaluation will be based on homework,
presentations and the final exam, with equal weight.
Graduate students will have extra work, which will be determined
once I see the enrollment.

**Scholastic offences:** Scholastic offences are taken
seriously and students are directed to read the appropriate policy,
specifically, the definition of what constitutes a Scholastic Offence,
at the following Web site:
http://www.uwo.ca/univsec/handbook/appeals/scholastic_discipline_grad.pdf