Author: Jonathan Rosenberg
Publisher: Springer Science & Business Media
ISBN: 1461243149
Category : Mathematics
Languages : en
Pages : 404
Book Description
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 Applications
Author: Jonathan Rosenberg
Publisher: Springer Science & Business Media
ISBN: 1461243149
Category : Mathematics
Languages : en
Pages : 404
Book Description
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.
Publisher: Springer Science & Business Media
ISBN: 1461243149
Category : Mathematics
Languages : en
Pages : 404
Book Description
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 Applications - Proceedings Of The School
Author: Hyman Bass
Publisher: World Scientific
ISBN: 9814544795
Category :
Languages : en
Pages : 622
Book Description
The Proceedings volume is divided into two parts. The first part consists of lectures given during the first two weeks devoted to a workshop featuring state-of-the-art expositions on 'Overview of Algebraic K-theory' including various constructions, examples, and illustrations from algebra, number theory, algebraic topology, and algebraic/differential geometry; as well as on more concentrated topics involving connections of K-theory with Galois, etale, cyclic, and motivic (co)homologies; values of zeta functions, and Arithmetics of Chow groups and zero cycles. The second part consists of research papers arising from the symposium lectures in the third week.
Publisher: World Scientific
ISBN: 9814544795
Category :
Languages : en
Pages : 622
Book Description
The Proceedings volume is divided into two parts. The first part consists of lectures given during the first two weeks devoted to a workshop featuring state-of-the-art expositions on 'Overview of Algebraic K-theory' including various constructions, examples, and illustrations from algebra, number theory, algebraic topology, and algebraic/differential geometry; as well as on more concentrated topics involving connections of K-theory with Galois, etale, cyclic, and motivic (co)homologies; values of zeta functions, and Arithmetics of Chow groups and zero cycles. The second part consists of research papers arising from the symposium lectures in the third week.
Algebraic K-Theory
Author: Vasudevan Srinivas
Publisher: Springer Science & Business Media
ISBN: 1489967354
Category : Science
Languages : en
Pages : 328
Book Description
Publisher: Springer Science & Business Media
ISBN: 1489967354
Category : Science
Languages : en
Pages : 328
Book Description
The $K$-book
Author: Charles A. Weibel
Publisher: American Mathematical Soc.
ISBN: 0821891324
Category : Mathematics
Languages : en
Pages : 634
Book Description
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 study of algebr
Publisher: American Mathematical Soc.
ISBN: 0821891324
Category : Mathematics
Languages : en
Pages : 634
Book Description
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 study of algebr
School on Algebraic K-theory and Its Applications
Author: Max Karoubi
Publisher:
ISBN:
Category : Homology theory
Languages : en
Pages : 554
Book Description
Publisher:
ISBN:
Category : Homology theory
Languages : en
Pages : 554
Book Description
K-Theory
Author: Max Karoubi
Publisher: Springer Science & Business Media
ISBN: 3540798900
Category : Mathematics
Languages : en
Pages : 337
Book Description
From the Preface: K-theory was introduced by A. Grothendieck in his formulation of the Riemann- Roch theorem. For each projective algebraic variety, Grothendieck constructed a group from the category of coherent algebraic sheaves, and showed that it had many nice properties. Atiyah and Hirzebruch considered a topological analog defined for any compact space X, a group K{X) constructed from the category of vector bundles on X. It is this ''topological K-theory" that this book will study. Topological K-theory has become an important tool in topology. Using K- theory, Adams and Atiyah were able to give a simple proof that the only spheres which can be provided with H-space structures are S1, S3 and S7. Moreover, it is possible to derive a substantial part of stable homotopy theory from K-theory. The purpose of this book is to provide advanced students and mathematicians in other fields with the fundamental material in this subject. In addition, several applications of the type described above are included. In general we have tried to make this book self-contained, beginning with elementary concepts wherever possible; however, we assume that the reader is familiar with the basic definitions of homotopy theory: homotopy classes of maps and homotopy groups.Thus this book might be regarded as a fairly self-contained introduction to a "generalized cohomology theory".
Publisher: Springer Science & Business Media
ISBN: 3540798900
Category : Mathematics
Languages : en
Pages : 337
Book Description
From the Preface: K-theory was introduced by A. Grothendieck in his formulation of the Riemann- Roch theorem. For each projective algebraic variety, Grothendieck constructed a group from the category of coherent algebraic sheaves, and showed that it had many nice properties. Atiyah and Hirzebruch considered a topological analog defined for any compact space X, a group K{X) constructed from the category of vector bundles on X. It is this ''topological K-theory" that this book will study. Topological K-theory has become an important tool in topology. Using K- theory, Adams and Atiyah were able to give a simple proof that the only spheres which can be provided with H-space structures are S1, S3 and S7. Moreover, it is possible to derive a substantial part of stable homotopy theory from K-theory. The purpose of this book is to provide advanced students and mathematicians in other fields with the fundamental material in this subject. In addition, several applications of the type described above are included. In general we have tried to make this book self-contained, beginning with elementary concepts wherever possible; however, we assume that the reader is familiar with the basic definitions of homotopy theory: homotopy classes of maps and homotopy groups.Thus this book might be regarded as a fairly self-contained introduction to a "generalized cohomology theory".
Motivic Homotopy Theory
Author: Bjorn Ian Dundas
Publisher: Springer Science & Business Media
ISBN: 3540458972
Category : Mathematics
Languages : en
Pages : 228
Book Description
This book is based on lectures given at a summer school on motivic homotopy theory at the Sophus Lie Centre in Nordfjordeid, Norway, in August 2002. Aimed at graduate students in algebraic topology and algebraic geometry, it contains background material from both of these fields, as well as the foundations of motivic homotopy theory. It will serve as a good introduction as well as a convenient reference for a broad group of mathematicians to this important and fascinating new subject. Vladimir Voevodsky is one of the founders of the theory and received the Fields medal for his work, and the other authors have all done important work in the subject.
Publisher: Springer Science & Business Media
ISBN: 3540458972
Category : Mathematics
Languages : en
Pages : 228
Book Description
This book is based on lectures given at a summer school on motivic homotopy theory at the Sophus Lie Centre in Nordfjordeid, Norway, in August 2002. Aimed at graduate students in algebraic topology and algebraic geometry, it contains background material from both of these fields, as well as the foundations of motivic homotopy theory. It will serve as a good introduction as well as a convenient reference for a broad group of mathematicians to this important and fascinating new subject. Vladimir Voevodsky is one of the founders of the theory and received the Fields medal for his work, and the other authors have all done important work in the subject.
Transcendental Aspects of Algebraic Cycles
Author: S. Müller-Stach
Publisher: Cambridge University Press
ISBN: 9780521545471
Category : Mathematics
Languages : en
Pages : 314
Book Description
Lecture notes for graduates or researchers wishing to enter this modern field of research.
Publisher: Cambridge University Press
ISBN: 9780521545471
Category : Mathematics
Languages : en
Pages : 314
Book Description
Lecture notes for graduates or researchers wishing to enter this modern field of research.
Algebraic K-Theory and its Geometric Applications
Author: Robert M.F. Moss
Publisher: Springer
ISBN: 3540361561
Category : Mathematics
Languages : en
Pages : 95
Book Description
Publisher: Springer
ISBN: 3540361561
Category : Mathematics
Languages : en
Pages : 95
Book Description
An Introduction to K-Theory for C*-Algebras
Author: M. Rørdam
Publisher: Cambridge University Press
ISBN: 9780521789448
Category : Mathematics
Languages : en
Pages : 260
Book Description
This book provides a very elementary introduction to K-theory for C*-algebras, and is ideal for beginning graduate students.
Publisher: Cambridge University Press
ISBN: 9780521789448
Category : Mathematics
Languages : en
Pages : 260
Book Description
This book provides a very elementary introduction to K-theory for C*-algebras, and is ideal for beginning graduate students.