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This section contains free e-books and guides on K theory, some of the resources in this section can be viewed online and some of them can be downloaded.

K theory Books
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Introduction To K theory and Some Applications

PDF | 141 Pages | English
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.

 
Lectures On K theory

PDF | 137 Pages | English
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.

 
A Geometric Introduction To K Theory

PDF | 285 Pages | English
This is one day going to be a textbook on K-theory, with a particular emphasis on connections with geometric phenomena like intersection multiplicities.

 
An Introduction To K theory

PDF | 78 Pages | English
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.

 
Lectures on K theory (PDF 95P)

PDF | 95 Pages | English
This lecture note covers the following topics: beginning of K theory, K theory of Banach algebras, Applications of topological Ktheory, The Atiyah- Singer index theorem, Algebraic K theory of Bass and Milnor applications, Higher Algebraic K theory, Hermitian K theory, Cyclic homology and K theory.

 
K Theory and Geometric Topology (PDF 37P)

PDF | 37 Pages | English
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.

 
Lectures on Topics in Algebraic K Theory (PDF 138P)

PDF | 138 Pages | English
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.

 
Lecture Notes on Algebraic K Theory (PDF 252P)

PDF | 252 Pages | English
This book covers the following topics: Categories and functors, Transformations and equivalences, Universal properties, Homotopy theory, Homotopy theory of categories, Waldhausen K-theory, Quillen K-theory, Abelian and exact categories.

 
Handbook of K theory

Online | NA Pages | English
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.

 
Algebraic K Theory (PDF 45P)

PDF | 45 Pages | English
This note introduces the definitions of the K-theory groups such as The group K0, The group K1, The group K2 and Higher K-theory groups.

 
Vector Bundles and K theory

Online | NA Pages | English
This book focusing on topological K-theory and containing also the necessary background material on vector bundles and characteristic classes.

 
An introduction to algebraic K Theory

Online | NA Pages | English
This book covers the following topics: Projective Modules and Vector Bundles, The Grothendieck group K_0, K_1 and K_2 of a ring, higher K-theory, The Fundamental Theorems of higher K-theory and the higher K-theory of Fields.

 
Complex Topological K Theory
Notes on K theory
The K book An Introduction to Algebraic K theory
Algebraic K theory
K Theory and Geometric Topology
Topological K theory and Algebraic Geometry
Clifford Modules and Twisted K Theory
LECTURE NOTES ON THE K THEORY OF OPERATOR ALGEBRAS
High dimensional knot theory
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