Introduction To Algebraic K Theory Am 72 Volume 72

Author : John Milnor
Publisher : Princeton University Press
Page : 200 pages
File Size : 55,8 Mb
Release : 2016-03-02
Category : Mathematics
ISBN : 9781400881796

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Introduction to Algebraic K-Theory. (AM-72), Volume 72 by John Milnor Pdf

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 out, in the present work, to define and study an analogous functor K2, also from associative rings to abelian groups. Just as functors K0 and K1 are important to geometric topologists, K2 is now considered to have similar topological applications. The exposition includes, besides K-theory, a considerable amount of related arithmetic.

Author : John W. Milnor
Publisher : Unknown
Page : 198 pages
File Size : 41,8 Mb
Release : 1971-01-01
Category : Electronic
ISBN : 0608064807

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Introduction to Algebraic K-Theory by John W. Milnor Pdf

Author : John Willard Milnor
Publisher : Princeton University Press
Page : 204 pages
File Size : 43,7 Mb
Release : 1971
Category : Mathematics
ISBN : 0691081018

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Introduction to Algebraic K-theory by John Willard Milnor Pdf

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 out, in the present work, to define and study an analogous functor K2, also from associative rings to abelian groups. Just as functors K0 and K1 are important to geometric topologists, K2 is now considered to have similar topological applications. The exposition includes, besides K-theory, a considerable amount of related arithmetic.

Author : Hyman Bass
Publisher : American Mathematical Soc.
Page : 68 pages
File Size : 48,9 Mb
Release : 1974-12-31
Category : Mathematics
ISBN : 9780821816707

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Introduction to Some Methods of Algebraic K-theory by Hyman Bass Pdf

Author : Richard G. Swan
Publisher : Springer
Page : 269 pages
File Size : 43,9 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540359173

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Algebraic K-Theory by Richard G. Swan Pdf

From the Introduction: "These notes are taken from a course on algebraic K-theory [given] at the University of Chicago in 1967. They also include some material from an earlier course on abelian categories, elaborating certain parts of Gabriel's thesis. The results on K-theory are mostly of a very general nature."

Author : Charles A. Weibel
Publisher : American Mathematical Soc.
Page : 634 pages
File Size : 51,5 Mb
Release : 2013-06-13
Category : Mathematics
ISBN : 9780821891322

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The $K$-book by Charles A. Weibel Pdf

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 : Daniel Scott Farley,Ivonne Johanna Ortiz
Publisher : Springer
Page : 148 pages
File Size : 52,6 Mb
Release : 2014-08-27
Category : Mathematics
ISBN : 9783319081533

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Algebraic K-theory of Crystallographic Groups by Daniel Scott Farley,Ivonne Johanna Ortiz Pdf

The Farrell-Jones isomorphism conjecture in algebraic K-theory offers a description of the algebraic K-theory of a group using a generalized homology theory. In cases where the conjecture is known to be a theorem, it gives a powerful method for computing the lower algebraic K-theory of a group. This book contains a computation of the lower algebraic K-theory of the split three-dimensional crystallographic groups, a geometrically important class of three-dimensional crystallographic group, representing a third of the total number. The book leads the reader through all aspects of the calculation. The first chapters describe the split crystallographic groups and their classifying spaces. Later chapters assemble the techniques that are needed to apply the isomorphism theorem. The result is a useful starting point for researchers who are interested in the computational side of the Farrell-Jones isomorphism conjecture, and a contribution to the growing literature in the field.

Author : Hvedri Inassaridze
Publisher : Springer Science & Business Media
Page : 444 pages
File Size : 40,9 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9789401585699

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Algebraic K-Theory by Hvedri Inassaridze Pdf

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 : Anonim
Publisher : American Mathematical Soc.
Page : 186 pages
File Size : 48,9 Mb
Release : 1991
Category : K-theory
ISBN : 0821873113

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Algebraic K-theory by Anonim Pdf

Author : Paul Frank Baum,Ralf Meyer,Rubén Sánchez-García,Marco Schlichting,Bertrand Toën
Publisher : Springer Science & Business Media
Page : 322 pages
File Size : 49,5 Mb
Release : 2010-11-05
Category : Mathematics
ISBN : 9783642157073

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Topics in Algebraic and Topological K-Theory by Paul Frank Baum,Ralf Meyer,Rubén Sánchez-García,Marco Schlichting,Bertrand Toën Pdf

This volume is an introductory textbook to K-theory, both algebraic and topological, and to various current research topics within the field, including Kasparov's bivariant K-theory, the Baum-Connes conjecture, the comparison between algebraic and topological K-theory of topological algebras, the K-theory of schemes, and the theory of dg-categories.

Author : A. A. Ambily,Roozbeh Hazrat,B. Sury
Publisher : Springer Nature
Page : 340 pages
File Size : 45,7 Mb
Release : 2020-01-17
Category : Mathematics
ISBN : 9789811516115

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Leavitt Path Algebras and Classical K-Theory by A. A. Ambily,Roozbeh Hazrat,B. Sury Pdf

The book offers a comprehensive introduction to Leavitt path algebras (LPAs) and graph C*-algebras. Highlighting their significant connection with classical K-theory—which plays an important role in mathematics and its related emerging fields—this book allows readers from diverse mathematical backgrounds to understand and appreciate these structures. The articles on LPAs are mostly of an expository nature and the ones dealing with K-theory provide new proofs and are accessible to interested students and beginners of the field. It is a useful resource for graduate students and researchers working in this field and related areas, such as C*-algebras and symbolic dynamics.

Author : Ottmar Loos,Erhard Neher
Publisher : Springer Nature
Page : 458 pages
File Size : 50,9 Mb
Release : 2020-01-10
Category : Mathematics
ISBN : 9781071602645

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Steinberg Groups for Jordan Pairs by Ottmar Loos,Erhard Neher Pdf

The present monograph develops a unified theory of Steinberg groups, independent of matrix representations, based on the theory of Jordan pairs and the theory of 3-graded locally finite root systems. The development of this approach occurs over six chapters, progressing from groups with commutator relations and their Steinberg groups, then on to Jordan pairs, 3-graded locally finite root systems, and groups associated with Jordan pairs graded by root systems, before exploring the volume's main focus: the definition of the Steinberg group of a root graded Jordan pair by a small set of relations, and its central closedness. Several original concepts, such as the notions of Jordan graphs and Weyl elements, provide readers with the necessary tools from combinatorics and group theory. Steinberg Groups for Jordan Pairs is ideal for PhD students and researchers in the fields of elementary groups, Steinberg groups, Jordan algebras, and Jordan pairs. By adopting a unified approach, anybody interested in this area who seeks an alternative to case-by-case arguments and explicit matrix calculations will find this book essential.

Author : F.E.A. Johnson
Publisher : Springer Science & Business Media
Page : 307 pages
File Size : 50,9 Mb
Release : 2011-11-17
Category : Mathematics
ISBN : 9781447122944

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Syzygies and Homotopy Theory by F.E.A. Johnson Pdf

The most important invariant of a topological space is its fundamental group. When this is trivial, the resulting homotopy theory is well researched and familiar. In the general case, however, homotopy theory over nontrivial fundamental groups is much more problematic and far less well understood. Syzygies and Homotopy Theory explores the problem of nonsimply connected homotopy in the first nontrivial cases and presents, for the first time, a systematic rehabilitation of Hilbert's method of syzygies in the context of non-simply connected homotopy theory. The first part of the book is theoretical, formulated to allow a general finitely presented group as a fundamental group. The innovation here is to regard syzygies as stable modules rather than minimal modules. Inevitably this forces a reconsideration of the problems of noncancellation; these are confronted in the second, practical, part of the book. In particular, the second part of the book considers how the theory works out in detail for the specific examples Fn ́F where Fn is a free group of rank n and F is finite. Another innovation is to parametrize the first syzygy in terms of the more familiar class of stably free modules. Furthermore, detailed description of these stably free modules is effected by a suitable modification of the method of Milnor squares. The theory developed within this book has potential applications in various branches of algebra, including homological algebra, ring theory and K-theory. Syzygies and Homotopy Theory will be of interest to researchers and also to graduate students with a background in algebra and algebraic topology.

Author : Helge Holden,Ragni Piene
Publisher : Springer Science & Business Media
Page : 561 pages
File Size : 44,5 Mb
Release : 2014-01-21
Category : Mathematics
ISBN : 9783642394492

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The Abel Prize 2008-2012 by Helge Holden,Ragni Piene Pdf

Covering the years 2008-2012, this book profiles the life and work of recent winners of the Abel Prize: · John G. Thompson and Jacques Tits, 2008 · Mikhail Gromov, 2009 · John T. Tate Jr., 2010 · John W. Milnor, 2011 · Endre Szemerédi, 2012. The profiles feature autobiographical information as well as a description of each mathematician's work. In addition, each profile contains a complete bibliography, a curriculum vitae, as well as photos — old and new. As an added feature, interviews with the Laureates are presented on an accompanying web site (http://extras.springer.com/). The book also presents a history of the Abel Prize written by the historian Kim Helsvig, and includes a facsimile of a letter from Niels Henrik Abel, which is transcribed, translated into English, and placed into historical perspective by Christian Skau. This book follows on The Abel Prize: 2003-2007, The First Five Years (Springer, 2010), which profiles the work of the first Abel Prize winners.

Author : Bruce A. Magurn
Publisher : Cambridge University Press
Page : 702 pages
File Size : 46,7 Mb
Release : 2002-05-20
Category : Mathematics
ISBN : 0521800781

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An Algebraic Introduction to K-Theory by Bruce A. Magurn Pdf

An introduction to algebraic K-theory with no prerequisite beyond a first semester of algebra.