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 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 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.
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 is one day
going to be a textbook on K-theory, with a particular emphasis on connections
with geometric phenomena like intersection multiplicities.