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This note covers the following topics: Recollections and preliminaries, Symmetric monoidal and stable categories, The group completion theorem and the K theory of finite fields, The K theory of stable categories.
Author(s): Fabian Hebestreit, University of Bonn
257Pages
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
92Pages
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
252Pages
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
NAPages
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
141Pages
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
137Pages
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
285Pages
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
37Pages
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): Olivier Isely
45Pages
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): Charles Weibel
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