High dimensional knot 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

Lectures On 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.

Author(s): Ioannis P. ZOIS

137 Pages