Math 443. Algebraic topology. Fall,
2015.
Textbook: Algebraic
topology by Allan
Hatcher, Cambridge
University Press, 2002.
- This book has been ordered at the university book store.
- The book is also available online at the
link above.
What you need to know to take this course. Some knowledge of topology is needed; the material in Math 240
or Math 440 will be adequate. It is more important to be comfortable with
algebra; the material in Math 436 will be assumed. You will need to
know about rings, modules, tensor products and Hom. These notions will
be defined when they are first needed in the course, but if you have never
seen them before, you may find the lectures hard to follow.
What is algebraic topology?
One answer to
this is that it is the use of algebra to tell topological spaces apart.
- How do we know that a torus (the
surface of a doughnut) is not homeomorphic to the 2-sphere?
- How can we be sure there is no
homeomorphism of R^3 that takes a knotted circle to an unknotted one?
- How do we know that the complete
graph on 5 points or the houses
and utilities graph cannot be embedded in the plane?
In each case algebraic topology gives
us a way to answer the question. For more information, see Essays about
algebraic topology.