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