Algebraic K Theory And Its Geometric Applications

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Algebraic K Theory And Its Geometric Applications

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Author : Robert M.F. Moss
language : en
Publisher: Springer
Release Date : 2006-11-15

Algebraic K Theory And Its Geometric Applications written by Robert M.F. Moss and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.

Algebraic K Theory And Its Applications

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Author : Jonathan Rosenberg
language : en
Publisher: Springer Science & Business Media
Release Date : 1995-12-22

Algebraic K Theory And Its Applications written by Jonathan Rosenberg and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-12-22 with Mathematics categories.

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.

Algebraic K Theory And Its Geometric Applications Lecture Notes In Mathematics 108

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Author :
language : en
Publisher:
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Algebraic K Theory And Its Geometric Applications Lecture Notes In Mathematics 108 written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.

Algebraic K Theory And Its Applications

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Author : Jonathan Rosenberg
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Algebraic K Theory And Its Applications written by Jonathan Rosenberg and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

Algebraic K-Theory plays an important role in many areas of modern mathematics: most notably algebraic topology, number theory, and algebraic geometry, but even including operator theory. The broad range of these topics has tended to give the subject an aura of inapproachability. This book, based on a course at the University of Maryland in the fall of 1990, is intended to enable graduate students or mathematicians working in other areas not only to learn the basics of algebraic K-Theory, but also to get a feel for its many applications. The required prerequisites are only the standard one-year graduate algebra course and the standard introductory graduate course on algebraic and geometric topology. Many topics from algebraic topology, homological algebra, and algebraic number theory are developed as needed. The final chapter gives a concise introduction to cyclic homology and its interrelationship with K-Theory.

Algebraic K Theory

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Author : Hvedri Inassaridze
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14

Algebraic K Theory written by Hvedri Inassaridze and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.

Algebraic K-theory is a modern branch of algebra which has many important applications in fundamental areas of mathematics connected with algebra, topology, algebraic geometry, functional analysis and algebraic number theory. Methods of algebraic K-theory are actively used in algebra and related fields, achieving interesting results. 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. It includes all principal algebraic K-theories, connections with topological K-theory and cyclic homology, applications to the theory of monoid and polynomial algebras and in the theory of normed algebras. This volume will be of interest to graduate students and research mathematicians who want to learn more about K-theory.

The Local Structure Of Algebraic K Theory

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Author : Bjørn Ian Dundas
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-09-06

The Local Structure Of Algebraic K Theory written by Bjørn Ian Dundas and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-09-06 with Mathematics categories.

Algebraic K-theory encodes important invariants for several mathematical disciplines, spanning from geometric topology and functional analysis to number theory and algebraic geometry. As is commonly encountered, this powerful mathematical object is very hard to calculate. Apart from Quillen's calculations of finite fields and Suslin's calculation of algebraically closed fields, few complete calculations were available before the discovery of homological invariants offered by motivic cohomology and topological cyclic homology. 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’. The usefulness of this theorem stems from being more accessible for calculations than K-theory, and hence a single calculation of K-theory can be used with homological calculations to obtain a host of ‘nearby’ calculations in K-theory. For instance, Quillen's calculation of the K-theory of finite fields gives rise to Hesselholt and Madsen's calculations for local fields, and Voevodsky's calculations for the integers give insight into the diffeomorphisms of manifolds. In addition to the proof of the full integral version of the local correspondence between K-theory and topological cyclic homology, the book provides an introduction to the necessary background in algebraic K-theory and highly structured homotopy theory; collecting all necessary tools into one common framework. It relies on simplicial techniques, and contains an appendix summarizing the methods widely used in the field. The book is intended for graduate students and scientists interested in algebraic K-theory, and presupposes a basic knowledge of algebraic topology.

Introduction To Algebraic K Theory

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Author : John Milnor
language : en
Publisher: Princeton University Press
Release Date : 2016-03-02

Introduction To Algebraic K Theory written by John Milnor and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-02 with Mathematics categories.

Algebraic K-theory describes a branch of algebra that centers about two functors. 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. Just as functors K0 and K1 are important to geometric topologists, K2 is now considered to have similar topological applications. The exposition includes, besides K-theory, a considerable amount of related arithmetic.

Algebraic K Theory Ii Proceedings Of The Conference Held At The Seattle Research Center Of Battelle Memorial Institute August 28 September 8 1972

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Author : Hyman Bass
language : en
Publisher: Springer
Release Date : 2006-11-15

Algebraic K Theory Ii Proceedings Of The Conference Held At The Seattle Research Center Of Battelle Memorial Institute August 28 September 8 1972 written by Hyman Bass and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.

Algebraic K Theory Iii Proceedings Of The Conference Held At The Seattle Research Center Of Battelle Memorial Institute August 28 September 8 1972

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Author : Hyman Bass
language : en
Publisher: Springer
Release Date : 2006-11-15

Algebraic K Theory Iii Proceedings Of The Conference Held At The Seattle Research Center Of Battelle Memorial Institute August 28 September 8 1972 written by Hyman Bass and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.

Algebraic K Theory I Proceedings Of The Conference Held At The Seattle Research Center Of Battelle Memorial Institute August 28 September 8 1972

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Author : Hyman Bass
language : en
Publisher: Springer
Release Date : 2006-11-15

Algebraic K Theory I Proceedings Of The Conference Held At The Seattle Research Center Of Battelle Memorial Institute August 28 September 8 1972 written by Hyman Bass and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.