Homotopy theory originated as a branch of topology in which one studied the ways in which geometrical shapes can be deformed. As it progressed the methods became quite sophisticated. One of the milestones was the realization that homotopy theoretic methods are useful in many other areas of mathematics, most notably in algebra and algebraic geometry. Because of this, an understanding of homotopy theory is quite valuable for mathematicians coming from different backgrounds. This course will focus on the original topological ideas of homotopy theory, and will prepare the student for further work, either within topology, or in other fields.

**Course outline:** This course is an introduction
to homotopy theory, which starts right at the beginning.
The choice of topics and the pace will depend
on the participants. We will cover the standard material, such
as fibrations, cofibre sequences, Whitehead theorems, the
Freudenthal suspension theorem, classifying spaces, etc., and will
end up talking about the Serre spectral sequence which
will allow us to do some computations of the homotopy groups of spheres.
An effort has been made to organize the material in a way
which emphasizes the geometrical ideas behind the results,
rather than the most efficient proofs or the most generality.

The course begins on Tuesday, April 27. Please contact me if you intend to come.

**Instructor:**Dan Christensen**E-mail:**jdc@uwo.ca**Office:**Middlesex 103b.**Office Phone:**661-2111 x86530.**Office Hours:**after class.**Class times and location:**Tuesdays and Thursdays, 1pm to 3pm in MC108. April 27 to July 15,**except May 4, 6 and June 8, 10**.**Prerequisites:**Algebraic topology (Math 414b) or permission of instructor.

**Text:** There is no text for the course, but
there is a list of books you may like
to refer to: dvi
or pdf.
Most of these are available in the library. I haven't
put them on reserve, so share with other students.
You are not required to buy any books for this course.

Allen Hatcher has a nice
book
on algebraic topology which also includes much of the homotopy
theory we will cover.
And the first chapter of his
book
on spectral sequences treats the Serre spectral sequence, which
will be the last topic of our course.
Both of these books can be **freely downloaded and printed**,
or can be purchased in bound form.

**Presentations:** In the second half of the semester,
each student will give one 50-55 minute presentation on a topic related
to the course. The scheduling will be worked out later.
Details: dvi or
pdf.

**Evaluation:** Homework will be due roughly every
two weeks. Evaluation will be based upon homework (65%)
and the presentations (35%). There will be no tests.