Math 443. Algebraic topology. Spring,
2002.
Textbook: Algebraic topology : a first course
by Greenberg and Harper,
Benjamin/Cummings Pub. Co., 1981.
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This book has been ordered at the university book store.
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Here is a link to the book at Barnes
& Noble
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.
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How do we know that a torus (the surface
of a doughnut) is not homeomorphic to the 2-sphere?
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How can we be sure there is no homeomorphism
of R^3 that takes a knotted circle to an unknotted one?
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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.
This page was last revised on December 17, 2001.
