Algebraic K-theory and its applications

by Rosenberg, J.

Publisher: Springer in New York

Written in English
Cover of: Algebraic K-theory and its applications | Rosenberg, J.
Published: Pages: 392 Downloads: 324
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Subjects:

  • K-theory.
  • Edition Notes

    Includes bibliographical references (p. [369]-376) and indexes.

    StatementJonathan Rosenberg.
    SeriesGraduate texts in mathematics ;, 147
    Classifications
    LC ClassificationsQA612.33 .R67 1996
    The Physical Object
    Paginationx, 392 p. :
    Number of Pages392
    ID Numbers
    Open LibraryOL536509M
    ISBN 100387942483, 3540942483
    LC Control Number96114570

The Mathematical Sciences Research Institute (MSRI), founded in , is an independent nonprofit mathematical research institution whose funding sources include the National Science Foundation, foundations, corporations, and more than 90 universities and institutions. The Institute is located at 17 Gauss Way, on the University of California, Berkeley campus, close to Grizzly Peak, on the. algebraic K-theory, and homotopy theory. Familiarity with these topics is important not just for a topology student but any student of pure mathe-matics, including the student moving towards research in geometry, algebra, or analysis. The prerequisites for a course based on this book include a workingFile Size: 3MB.   A First Book in Algebra, by Wallace C. Boyden; Theory of Groups of Finite Order, by William Burnside Algebraic K-Theory and Its Applications,Jonathan Rosenberg. Algebraic Number Theory,Serge : Kevin de Asis. Writings. With Eric Friedlander, An overview over algebraic K-theory, in Algebraic K-theory and its applications, World Scientific , pp. 1– ( Trieste Lecture Notes); Weibel, Charles A. (), The K-book, Graduate Studies in Mathematics, , American Mathematical Society, Providence, RI, ISBN , MR With Carlo Mazza, Vladimir Voevodsky Lectures on Motivic.

When the algebraic K-theory group NK_1(ZG) is nontrivial (e.g., for G=Z/4), we show the dynamical zeta function for any such extension is consistent with infinitely many topological conjugacy classes. A Concise Course in Algebraic Topology (J. P. May) This book explains the following topics: The fundamental group and some of its applications, Categorical language and the van Kampen theorem, Covering spaces, Graphs, Compactly generated spaces, Cofibrations, Fibrations, Based cofiber and fiber sequences, Higher homotopy groups, CW complexes. I have now returned to an earlier plan of having this material be an extra chapter of the Algebraic Topology book, rather than a separate book. The current version of this chapter is here. Its main focus is the Serre spectral sequence and its applications, but there is also some coverage of the Adams spectral sequence and, more briefly, a few. The theme of this book is infinite loop space theory and its multiplicative elaboration. The main goal is a complete analysis of the relationship between the classifying spaces of geometric topology and the infinite loop spaces of algebraic K-theory. ( views) The Homology of Iterated Loop Spaces by F. R. Cohen, T. J. Lada, P. J. May.

  Algebraic \(K\)-theory, which is the main character of this book, deals mainly with studying the structure of rings. However, it turns out that even working in a purely algebraic context, one requires techniques from homotopy theory to construct the . On the Farrell-Jones Conjecture and its applications ArthurBartels,WolfgangLu¨ckandHolgerReich Abstract. We present the status of the Farrell-Jones Conjecture for algebraic K-theory for a group Gand arbitrary coefficient rings R. We add new groups for which the conjec-ture is known to be true and study inheritance properties. We discuss new. And is there material (lecture Video or good pdf script) where the algebraic K-theory is explained? Nothing very accessible for algebraic K-theory. Blackadar's book for K-theory of operator algebras, and Atiyah's book for topological K-theory as it stood in the 's, are readable without a lot of algebraic . Then you may have a look at Blackadar's book "K-Theory for Operator Algebras", Lemma If you have the definition by finiteily generated projective modules in mind, have a look at Rosenbergs Book "Algebraic K-Theory and its applications", Lemma $\endgroup$ – Epsilon Apr 14 '19 at

Algebraic K-theory and its applications by Rosenberg, J. Download PDF EPUB FB2

Buy Algebraic K-Theory and Its Applications (Graduate Texts in Mathematics) (v. ) on FREE SHIPPING on qualified orders Algebraic K-Theory and Its Applications (Graduate Algebraic K-theory and its applications book in Mathematics) (v.

): Rosenberg, Jonathan: : BooksCited by: 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 by: Algebraic K-Theory and Its Applications (Graduate Texts in Mathematics, No.

) [Jonathan Rosenberg] on *FREE* shipping on qualifying offers.5/5(1). This book, based on a course at the University of Maryland in the fall ofis 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 : Springer-Verlag New York.

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/5(2).

This book, based on a course at the University of Maryland in the fall ofis 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.

Book Description Algebraic K-theory is a discipline which is internally coherent, but has strong connections to diverse mathematical disciplines, and has contributed solutions to problems in algebra, number theory, analysis, geometry and functional analysis. It even has links to particle by: 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 Algebraic K-theory and its applications book theory.

Methods of algebraic K-theory are actively used in algebra and related fields, achieving interesting results. Algebraic K-Theory and Its Applications.

Proceedings of the Workshop and Symposium. 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.

Some applications Non-vanishing of class groups and Whitehead groups Idempotents in C*-algebras Group rings and assembly maps References Books and Monographs on Related Areas of Algebra, Analysis, Number Theory, and Topology Books and Monographs on Algebraic if-Theory Specialized References Notational Index Book Description Algebraic K-theory is a discipline which is internally coherent, but has strong connections to diverse mathematical disciplines, and has contributed solutions to problems in algebra, number theory, analysis, geometry and functional analysis.

It even has links to particle physics.5/5(1). Algebraic K-Theory and Its Applications. Algebraic K-Theory and Its Applications. Jonathan Rosenberg. Springer Science & Business Media, - Mathematics - pages. 2 Reviews. Algebraic K-Theory plays an important role 5/5(1).

In I wrote out a brief outline, following Quillen's paper Higher algebraic K-theory I. It was overwhelming. I talked to Hy Bass, the author of the classic book Algebraic K-theory, about what would be involved in writing such a book. It was scary, because (in ) I didn't know even how to write a book.

For the Higher Algebraic K-Theory there are the books by Jonathan Rosenberg: ”Algebraic K-Theory and its Applications”, Springer Graduate Texts inMathematics (), thebookby as: ”Algebraic K-Theory”, Birkhauser, Boston () and the book by Hvedri Inassaridze: ”Algebraic K.

This book, based on a course at the University of Maryland in the fall ofis intended to enable graduate students or mathematicians working in other areas not only to learn the basics of.

Introduction To K theory and Some Applications. 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.

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 s of algebraic K-theory are actively used in algebra and related fields, achieving interesting results.

This book presents the elements of algebraic K-theory, Brand: Springer Netherlands. "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. Algebraic K-Theory is crucial in many areas of modern mathematics, especially algebraic topology, number theory, algebraic geometry, and operator theory. Topics include algebraic topology, homological algebra, algebraic number theory, and an introduction to cyclic homology and its.

Algebraic K-Theory and its Applications by Jonathan Rosenberg Errata to the Second Printing, I am quite grateful to those who have sent me their comments on this book. I especially thank Paul Arne Ostvaer, Ioannis Emmanouil, Desmond Sheiham, Efton Park, Jon Berrick, Henrik Holm, Mike Boyle, and Hanfeng Li for their corrections.

Chapter I. Summary: Algebraic K-Theory is crucial in many areas of modern mathematics, especially algebraic topology, number theory, algebraic geometry, and operator theory.

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. Editors: Moss, Robert M.F., Thomas, Charles B. (Eds.) Free Preview. 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 s of algebraic K-theory are actively used in algebra and related fields, achieving interesting results.

This book presents the elements of algebraic K-theory. Algebra and Applications aims to publish well-written and carefully refereed monographs with up-to-date expositions of research in all fields of algebra, including its classical impact on commutative and noncommutative algebraic and differential geometry, K-theory and algebraic topology, and further applications in related domains, such as number theory, homotopy and (co)homology theory.

This book provides an accessible introduction to algebraic topology, a field at the intersection of topology, geometry and algebra, together with its applications. Moreover, it covers several related topics that are in fact important in the overall scheme of algebraic topology.

K -theory was invented in the late s by Alexander Grothendieck in his study of intersection theory on algebraic varieties. In the modern language, Grothendieck defined only K0, the zeroth K -group, but even this single group has plenty of applications, such as the Grothendieck–Riemann–Roch theorem.

A survey of higher K-theory Cyclic homology and its relation to K-Theory Basics of cyclic homology The Chern character Some applications --References --Books and Monographs on Related Areas of Algebra, Analysis, Number Theory, and Topology --Books and Monographs on Algebraic K-Theory --Specialized References --Notational Index.

Algebraic K-theory and Its Applications: Proceedings of the Workshop and Symposium: ICTP, Trieste, Italy, September Algebraic K Theory And Its Applications. 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.

Dominique Arlettaz, Algebraic K-theory of rings from a topological viewpoint. Daniel Grayson, Quillen’s work in algebraic K-theory, J.

K-Theory 11 (), – pdf. An introductory textbook account is in. Charles Weibel, The K-Book: An introduction to algebraic K-theory ; Further review includes.An Algebraic Introduction to K-Theory This book is an introduction to K-theory and a text in algebra. These two roles are entirely compatible.

On the one hand, nothing more than the basic algebra of groups, rings, and modules is needed to explain the classical algebraic K-theory.

On the other.Algebraic K-theory allows you to talk about characteristic classes of vector bundles on schemes, with values in various cohomology theories, see for example Gillet: K-theory and algebraic geometry. Algebraic K-theory is intimately connected with motivic cohomology and algebraic cycles, see for example Friedlander's ICTP lectures available on.