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Friday, May 15, 2020 | History

4 edition of Algebraic K-theory and its applications found in the catalog.

Algebraic K-theory and its applications

Jonathan Rosenberg

Algebraic K-theory and its applications

by Jonathan Rosenberg

  • 373 Want to read
  • 26 Currently reading

Published by Springer in New York .
Written in


Edition Notes

StatementJonathan Rosenberg.
SeriesGraduate texts in mathematics -- 147
The Physical Object
Paginationx,392p. ;
Number of Pages392
ID Numbers
Open LibraryOL22592953M
ISBN 100387942483, 3540942483

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.


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Algebraic K-theory and its applications by Jonathan Rosenberg 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 Texts 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 number 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.