This lecture note covers the following topics:Projections and
Unitaries, The K0-Group for Unital C -Algebras, K1-Functor and the Index Map,
Bott Periodicity and the Exact Sequence of K-Theory, Tools for the computation
This note explains the following topics: Categories and functors, Transformations and
equivalences, Universal properties, Homotopy theory, Simplicial methods,
Homotopy theory of categories, Waldhausen K-theory, Abelian and exact
categories, Quillen K-theory.
covers the following topics: Some homotopy theory, Exact categories,
Q-construction, Fundamental groupoid, Waldhausen's constructions, Additivity,
The K-theory spectrum, Products, Group completion, Q=+ theorem, The defining
acyclic map, Homotopy fibres, Resolution theorem, Dévissage, Abelian category
localization, Coherent sheaves and open subschemes, Product formulas, K-theory
with finite coefficients, Homology, K-theory of graded rings, Homotopy property,
Rigidity, K-theory of finite fields.
This note explains the following topics: Algebraic
K-theory, Gamma-spaces and S-algebra, Reductions, Topological Hochschild
homology, The trace K, Topological Cyclic homology, The comparison of K-theory
and TC, Homotopical foundations.
Author(s):Bjorn Ian Dundas, Thomas G. Goodwillie and
This note descibes the
following topics: Vector bundles, Characteristic classes, K-theory, The functor
K, The fundamental product theorem, The Mayer–Vietoris sequence, Structure of
K-theory, The yoga of symmetric polynomials.
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.
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.