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.
This book explains the following topics: Topological K-theory, K-theory of
C* algebras , Geometric and Topological Invarients, THE FUNCTORS K1 K2, K1, SK1
of Orders and Group-rings, Higher Algebraic K-theory , Higher Dimensional Class
Groups of Orders and Group rings , Higher K-theory of Schemes, Mod-m Higher
K-theory of exact Categories, Schemes and Orders, Profinite Higher K-theory of
Exact Categories, Schemes and Orders, Equivariant Higher K-theory Together with
Relative Generalizations, Interpretation in Terms of Group-rings.
This book covers the following topics:
Topological K-Theory, Topological Preliminaries on Vector Bundles, Homotopy,
Bott Periodicity and Cohomological Properties, Chern Character and Chern
Classes, Analytic K-Theory, Applications of Adams operations, Higher Algebraic
K-Theory, Algebraic Preliminaries and the the Grothendieck
Group, The Whitehead and the Steinberg Groups.
This lecture note covers the following topics: beginning of K theory,
K theory of Banach algebras, Applications of topological Ktheory, The Atiyah-
Singer index theorem, Algebraic K theory of Bass and Milnor applications,
Higher Algebraic K theory, Hermitian K theory, Cyclic homology and K 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.
two-volume handbook offers a compilation of techniques and results in
K-theory. These two volumes consist of chapters, each of which is
dedicated to a specific topic and is written by a leading expert.
This book covers the following topics: Projective Modules and Vector Bundles, The Grothendieck group K_0, K_1 and
K_2 of a ring, higher K-theory, The Fundamental Theorems of higher K-theory
and the higher K-theory of Fields.