This note will develop the
K-theory of Banach algebras, the theory of extensions of C algebras, and the
operator K-theory of Kasparov from scratch to its most advanced aspects. Topics
covered includes: Survey of Topological K-Theory, Operator K-Theory,
Preliminaries, K-theory Of Crossed Products, Theory Of Extensions, Kasparovís Kk-theory.
note covers the following topics: The exact
sequence of algebraic K-theory, Categories of modules and their equivalences,
Brauer group of a commutative ring, Brauer-Wall group of graded Azumaya
algebras and The structure of the Clifford Functor.
book covers the following topics: Categories and functors, Transformations and equivalences, Universal
properties, Homotopy theory, Homotopy theory of categories, Waldhausen
K-theory, Quillen K-theory, Abelian and exact categories.