Handbook of K theory

Lecture Notes On The K theory Of Operator Algebras

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.

Author(s): Rainer Matthes and Wojciech Szymansk

92 Pages

Lecture Notes on Algebraic K Theory by John Rognes

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.

Author(s): John Rognes

252 Pages

Lectures on Algebraic K theory by J.F. Jardine

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.

Author(s): J.F. Jardine

NA Pages

Introduction To K theory and Some Applications

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.

Author(s): Aderemi Kuku, University of Iowa

141 Pages