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The local structure of algebraic K theory
This note explains the following topics: Algebraic K-theory, Gamma-spaces and S-algebra, Reductions, Topological Hochschild homology, The trace K, Topological Cyclic homology, The comparison of K-theory and TC, Homotopical foundations.
Author(s): Bjorn Ian Dundas, Thomas G. Goodwillie and Randy McCarthy
424 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 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
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): Daniel Dugger
285 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
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): Max Karoubi
95 Pages
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): John Rognes
252 Pages
The K book An Introduction to Algebraic K theory
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Author(s): NA
NA Pages
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NA Pages
K Theory and Geometric Topology
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NA Pages
Clifford Modules and Twisted K Theory
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