Transformation Groups And Algebraic K Theory PDF Download
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Author | : Wolfgang Lück |
Publisher | : Springer |
Total Pages | : 455 |
Release | : 2006-11-14 |
Genre | : Mathematics |
ISBN | : 3540468277 |
Download Transformation Groups and Algebraic K-Theory Book in PDF, ePub and Kindle
The book focuses on the relation between transformation groups and algebraic K-theory. The general pattern is to assign to a geometric problem an invariant in an algebraic K-group which determines the problem. The algebraic K-theory of modules over a category is studied extensively and appplied to the fundamental category of G-space. Basic details of the theory of transformation groups sometimes hard to find in the literature, are collected here (Chapter I) for the benefit of graduate students. Chapters II and III contain advanced new material of interest to researchers working in transformation groups, algebraic K-theory or related fields.
Author | : Vasudevan Srinivas |
Publisher | : Springer Science & Business Media |
Total Pages | : 328 |
Release | : 2013-11-21 |
Genre | : Science |
ISBN | : 1489967354 |
Download Algebraic K-Theory Book in PDF, ePub and Kindle
Author | : Charles A. Weibel |
Publisher | : American Mathematical Soc. |
Total Pages | : 634 |
Release | : 2013-06-13 |
Genre | : Mathematics |
ISBN | : 0821891324 |
Download The $K$-book Book in PDF, ePub and Kindle
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
Author | : Hvedri Inassaridze |
Publisher | : Springer Science & Business Media |
Total Pages | : 444 |
Release | : 2013-03-14 |
Genre | : Mathematics |
ISBN | : 9401585695 |
Download Algebraic K-Theory Book in PDF, ePub and Kindle
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.
Author | : Jonathan Rosenberg |
Publisher | : Springer Science & Business Media |
Total Pages | : 404 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461243149 |
Download Algebraic K-Theory and Its Applications Book in PDF, ePub and Kindle
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.
Author | : Wayne Raskind |
Publisher | : American Mathematical Soc. |
Total Pages | : 330 |
Release | : 1999 |
Genre | : Mathematics |
ISBN | : 082180927X |
Download Algebraic $K$-Theory Book in PDF, ePub and Kindle
This volume presents the proceedings of the Joint Summer Research Conference on Algebraic K-theory held at the University of Washington in Seattle. High-quality surveys are written by leading experts in the field. Included is an up-to-date account of Voevodsky's proof of the Milnor conjecture relating the Milnor K-theory of fields to Galois cohomology. The book is intended for graduate students and research mathematicians interested in $K$-theory, algebraic geometry, and number theory.
Author | : Bjørn Ian Dundas |
Publisher | : Springer Science & Business Media |
Total Pages | : 447 |
Release | : 2012-09-06 |
Genre | : Mathematics |
ISBN | : 1447143930 |
Download The Local Structure of Algebraic K-Theory Book in PDF, ePub and Kindle
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.
Author | : Emilio Lluis-Puebla |
Publisher | : Springer |
Total Pages | : 172 |
Release | : 2006-11-14 |
Genre | : Mathematics |
ISBN | : 3540466398 |
Download Higher Algebraic K-Theory: An Overview Book in PDF, ePub and Kindle
This book is a general introduction to Higher Algebraic K-groups of rings and algebraic varieties, which were first defined by Quillen at the beginning of the 70's. These K-groups happen to be useful in many different fields, including topology, algebraic geometry, algebra and number theory. The goal of this volume is to provide graduate students, teachers and researchers with basic definitions, concepts and results, and to give a sampling of current directions of research. Written by five specialists of different parts of the subject, each set of lectures reflects the particular perspective ofits author. As such, this volume can serve as a primer (if not as a technical basic textbook) for mathematicians from many different fields of interest.
Author | : Hyman Bass |
Publisher | : World Scientific |
Total Pages | : 622 |
Release | : 1999-03-12 |
Genre | : |
ISBN | : 9814544795 |
Download Algebraic K-theory And Its Applications - Proceedings Of The School Book in PDF, ePub and Kindle
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.
Author | : Bruce A. Magurn |
Publisher | : Cambridge University Press |
Total Pages | : 702 |
Release | : 2002-05-20 |
Genre | : Mathematics |
ISBN | : 9780521800785 |
Download An Algebraic Introduction to K-Theory Book in PDF, ePub and Kindle
An introduction to algebraic K-theory with no prerequisite beyond a first semester of algebra.