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Tuesday, July 21, 2020 | History

2 edition of Algebraic K-theory .... found in the catalog.

Algebraic K-theory ....

Hyman Bass

Algebraic K-theory ....

by Hyman Bass

  • 107 Want to read
  • 19 Currently reading

Published by Benjamin in New York .
Written in English


Edition Notes

SeriesMathematics Lecture Note Ser
ID Numbers
Open LibraryOL20221356M

An introduction to algebraic K Theory. This book covers the following topics: Projective Modules and Vector Bundles, The Grothendieck group K_0, K_1 and K_2 of a ring, higher K-theory, The Fundamental Theorems of higher K-theory and the higher K-theory of Fields. Author(s): Charles Weibel.   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 : Hvedri Inassaridze.

This book contains accounts of talks held at a symposium in honor of John C. Moore in October at Princeton University, The work includes papers in classical homotopy theory, homological algebra, rational homotopy theory, algebraic K-theory of spaces, and other subjects. The Local Structure of Algebraic K-Theory // Kindle ^ ZLBABK1IMW The Local Structure of Algebraic K-Theory By Bjørn Ian Dundas Springer Okt , Taschenbuch. Book Condition: Neu. xx24 mm. This item is printed on demand - Print on Demand Titel. Neuware - Algebraic K-theory encodes important invariants for several mathematical.

Important topics related to Bass's mathematical interests are surveyed by leading experts in the field. Of particular note is a professional autobiography of Professor Bass and an article by Deborah Ball on mathematical education. The range of subjects covered in the book offers a convenient single source for topics in the field. In mathematics, topological K-theory is a branch of algebraic was founded to study vector bundles on topological spaces, by means of ideas now recognised as (general) K-theory that were introduced by Alexander early work on topological K-theory is due to Michael Atiyah and Friedrich Hirzebruch.


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Algebraic K-theory ... by Hyman Bass Download PDF EPUB FB2

I talked to Hy Bass, the Algebraic K-theory. book 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. I needed a warm-up exercise, a practice book if you will.

The result, An introduction to homological algebra, took over five years to write. 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 higher K-groups and to perform computations.

The resulting interplay of algebra, geometry, and Cited by: This book gives a superb overview of algebraic K-theory, and could be read by anyone who has taken a course in commutative algebra or a course in the theory of rings.

The reader will see a common theme throughout algebraic K-theory, namely that of abelianization, which is Cited by: From the Introduction: "These notes are taken from a course on algebraic K-theory [given] at the University of Chicago in They also include some material from an earlier course on abelian categories, elaborating certain parts of Gabriel's thesis.

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 ofis intended to enable graduate 5/5(1). 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 Algebraic K-theory. book, in the present work, to define and study an analogous functor K2, also from associative rings to abelian 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.

In mathematics, K-theory is, roughly speaking, the study of a ring generated by vector bundles over a topological space or algebraic topology, it is a cohomology theory known as topological algebra and algebraic geometry, it is referred to as algebraic is also a fundamental tool in the field of operator can be seen as the study of certain kinds of.

from Motivic Cohomology to K-theory in §4 and use it in §6–10 to describe the K-theory of local and global fields. The Back Story: InI started hearing a persistent rumor that I was writing a book on algebraic K-theory.

This was a complete surprise to me. Someone else had started the rumor, and I never knew who. 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 higher \(K\)-groups and to perform computations. The homotopy theory of vector bundles, and topological k-theory, then provide a completely satisfactory framework within which to treat such questions.

It is remarkable that there exists, in algebra, nothing remotely comparable depth or generality, even though many of these questions are algebraic in character. excerpt from book's IntroductionAuthor: Hyman Bass.

A NATO Advanced Study Institute entitled "Algebraic K-theory and Algebraic Topology" was held at Chateau Lake Louise, Lake Louise, Alberta, Canada from December 12 to December 16 of This book is the volume of proceedings for this meeting.

The. Algebraic K-theory | Daniel R. Grayson | download | B–OK. Download books for free. Find books. I suggest looking at the introduction to Waldhausen's original paper on algebraic K-theory (Algebraic K-theory of generalized free products, Part I, Ann.

Math., () ). Waldhausen started out as a 3-manifold theorist, and he realized that certain phenomena in the topology of 3-manifolds would be explained if the Whitehead groups of.

Algebraic K-Theory (Lecture Notes in Mathematics) th Edition by Richard G. Swan (Author) ISBN ISBN Why is ISBN important. ISBN. This bar-code number lets you verify that you're getting exactly the right version or edition of a book. The digit and digit formats both 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 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. 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.

The K-book: An introduction to algebraic K-theory by Charles Weibel. Publisher: Rutgers Description: Algebraic K-theory is an important part of homological algebra. From the table of contents: Projective Modules and Vector Bundles; The Grothendieck group K_0; K_1 and K_2 of a ring; Definitions of higher K-theory; The Fundamental Theorems of higher K-theory.

Algebraic K-Theory has become an increasingly active area of research. With its connections to algebra, algebraic geometry, topology, and number theory, it has implications for a wide variety of researchers and graduate students in mathematics. The book is based on lectures given at the author'sBrand: Birkhäuser Basel.

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.

About this book Introduction These are notes from a graduate student course on algebraic topology and K-theory given by Daniel Quillen at the Massachusetts Institute of Technology during Buy Transformation Groups and Algebraic K-Theory online at best price in India on Snapdeal.

Read Transformation Groups and Algebraic K-Theory reviews & author details. Get Free shipping & CoD options across : ₹An exposition of K-theory and cyclic cohomology. It begins with examples of various situations in which the K-functor of Grothendieck appears naturally, including the topological and algebraic K-theory, K-theory of C*-algebras, and K-homology.

( views) The K-book: An introduction to algebraic K-theory by Charles Weibel - Rutgers,