This note
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 covers the following topics: Recollections and
preliminaries, Symmetric monoidal and stable categories, The group completion
theorem and the K theory of finite fields, The K theory of stable categories.
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
of K-groups.
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 is one day
going to be a textbook on K-theory, with a particular emphasis on connections
with geometric phenomena like intersection multiplicities.