/   Mathematics Books /  

Topology Books / K theory Books

K theory Books

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 Notes

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):

s 97Pages

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, Kasparovís Kk-theory.

Author(s):

s 314Pages

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):

s 141Pages

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):

s 137Pages

A Geometric Introduction To K Theory

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

Author(s):

s 285Pages

An Introduction To K theory

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):

s 78Pages

Lectures on K theory (PDF 95P)

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.

Author(s):

s 95Pages

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):

s 37Pages

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):

s 138Pages

Lecture Notes on Algebraic K Theory (PDF 252P)

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.

Author(s):

s 252Pages

Handbook of K theory

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):

s NAPages

Algebraic K Theory (PDF 45P)

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.

Author(s):

s 45Pages

Vector Bundles and K theory

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

Author(s):

s NAPages

An introduction to algebraic K Theory

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.

Author(s):

s NAPages

Complex Topological K Theory

Currently this section contains no detailed description for the page, will update this page soon.

Author(s):

s NAPages

Notes on K theory

Currently this section contains no detailed description for the page, will update this page soon.

Author(s):

s NAPages

The K book An Introduction to Algebraic K theory

Currently this section contains no detailed description for the page, will update this page soon.

Author(s):

s NAPages

Algebraic K theory

Currently this section contains no detailed description for the page, will update this page soon.

Author(s):

s NAPages

K Theory and Geometric Topology

Currently this section contains no detailed description for the page, will update this page soon.

Author(s):

s NAPages

Clifford Modules and Twisted K Theory

Currently this section contains no detailed description for the page, will update this page soon.

Author(s):

s NAPages

High dimensional knot theory

Currently this section contains no detailed description for the page, will update this page soon.

Author(s):

s NAPages