# Algebraic topology, Math 414b/501b, Winter 2008

## The final exam is Wednesday, April 23, 2-5 pm, MC107.

Algebraic topology is the study of topological spaces using
tools of an algebraic nature, such as homology groups,
cohomology groups and homotopy groups.
It is one of the major accomplishments of twentieth century
mathematics and has applications to many areas of mathematics and to
other fields, such as physics, computer science, and economics.
This is a first course in algebraic topology which will
introduce the invariants mentioned above, explain
their basic properties and develop geometric intuition
and methods of computation.
**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:** 661-2111 x86530.
**Office Hours:** to be determined.
**Class times and location:**
Mondays 11:30-12:35 and
Wednesdays 11:30-12:55 in MC108.
**Prerequisites:** Group Theory (Math 302a)
and General Topology (Math 404a).
**Web page:** This page is available at
http://jdc.math.uwo.ca/M414/,
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.

Here is a list of other reading material.
None of these are required, but you might find them interesting.
A few are on reserve at the library.

**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
show your written work to others.
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 won't be accepted unless arranged in advance
for a good reason.

**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 at
the end of the course: **Wednesday, April 23, 2-5 pm, MC107**.

**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.

Back to Dan Christensen's home page.

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