Algebraic K-Theory is crucial in many areas of modern mathematics, especially algebraic topology, number theory, algebraic geometry, and operator theory. This text is designed to help graduate students in other areas learn the basics of K-Theory and get a feel for its many applications. Topics include algebraic topology, homological algebra, algebraic number theory, and an introduction to cyclic homology and its interrelationship with K-Theory.
This book presents the elements of algebraic K-theory, based essentially on the fundamental works of Milnor, Swan, Bass, Quillen, Karoubi, Gersten, Loday and Waldhausen.
J.-L. Brylinski and S. Zucker, An overview of recent advances in Hodge theory, Encycl. of Math. Sciences, vol. 69, Springer - Verlag, Berlin - Heidelberg ... J.W.Hoffmann, The Hodge theory of stable curves, Mem. Amer. Math. Soc., vol.
Algebraic K-Theory and its Geometric Applications
An introduction to algebraic K-theory with no prerequisite beyond a first semester of algebra.
"It is a pleasure to read this mathematically beautiful book..." ---WW.J. Julsbergen, Mathematics Abstracts "The book does an admirable job of presenting the details of Quillen's work..." ---Mathematical Reviews
K0 and K1, which assign to each associative ring ∧ an abelian group K0∧ or K1∧ respectively. Professor Milnor sets out, in the present work, to define and study an analogous functor K2, also from associative rings to abelian groups.
This book covers the connection between algebraic K-theory and Bökstedt, Hsiang and Madsen's topological cyclic homology and proves that the difference between the theories are ‘locally constant’.
Informally, $K$-theory is a tool for probing the structure of a mathematical object such as a ring or a topological space in terms of suitably parameterized vector spaces and producing important intrinsic invariants which are useful in the ...
K0 and K1, which assign to each associative ring ∧ an abelian group K0∧ or K1∧ respectively. Professor Milnor sets out, in the present work, to define and study an analogous functor K2, also from associative rings to abelian groups.
Algebraic K-theory: From the Seminar on Algebraic K-Theory Held at Leningrad State University by A. A. Suslin