Math 583G K-theory
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Math 583G. K-theory. Steve Mitchell. Spring 2008. Monday/Wednesday/Friday 2:30. This course will be offered in the Spring with Jack Lee’s Winter course on …
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Content
Math 583G
K-theory
Steve Mitchell
Spring 2008
Monday/Wednesday/Friday 2:30
This course will be offered in the Spring with Jack Lee’s Winter course on fiber bundles as
a prerequisite. It is of interest to students in topology, differential geometry, and algebraic
geometry.
K-theory is a beautiful subject that is unfortunately stuck with an ugly name.1 From the
topological point of view, it originates in the following way: Let X be a space and let
V ectX denote the set of isomorphism classes of real or complex vector bundles over X.
These form an abelian monoid under the Whitney sum operation (fiber-wise direct sum).
Since monoids are bad and groups are good, we formally “complete” V ectX by adjoining
inverses, in much the same way that the integers are constructed from the natural
numbers. This is the abelian group K(X)-the (real or complex) K-theory of X.
Topics to be covered include the following:
?Bott periodicity. The remarkable Bott periodicity theorem computes the groups
K(Sn), showing in particular that they are periodic in n, where the period is 2 in
the complex case and 8 in the real…
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Related Searches: bott periodicity, periodicity theorem, differential geometry, mitchell spring, vector bundles
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