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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
Characteristic classes and K theory
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.
Author(s): Oscar Randal-Williams
62 Pages
This note covers the following topics: Vector Bundles and Bott Periodicity, K-theory Represented by Fredholm Operators, Representations of Compact Lie Groups, Equivariant K-theory.
Author(s): Arun Debray
97 Pages
K theory For Operator Algebras
This note will develop the K-theory of Banach algebras, the theory of extensions of C algebras, and the operator K-theory of Kasparov from scratch to its most advanced aspects. Topics covered includes: Survey of Topological K-Theory, Operator K-Theory, Preliminaries, K-theory Of Crossed Products, Theory Of Extensions, Kasparov’s Kk-theory.
Author(s): Bruce Blackadar
314 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
This note provides an overview of various aspects of algebraic K-theory, with the intention of making these lectures accessible to participants with little or no prior knowledge of the subject.
Author(s): Eric Friedlander
78 Pages
K Theory and Geometric Topology (PDF 37P)
The primary purpose of this note is to examine many of these K-theoretic invariants, not from a historical point of view, but rather a posteriori, now that K-theory is a mature subject.
Author(s): Jonathan Rosenberg
37 Pages
Lectures on Topics in Algebraic K Theory (PDF 138P)
This 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.
Author(s): Hyman Bass
138 Pages
This 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.
Author(s): NA
NA Pages
This book focusing on topological K-theory and containing also the necessary background material on vector bundles and characteristic classes.
Author(s): Allen Hatcher
NA Pages
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Author(s): NA
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Clifford Modules and Twisted K Theory
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Author(s): NA
NA Pages
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