Algebraic K Theory Of Crystallographic Groups

Author : Daniel Scott Farley
Publisher : Springer
ISBN 13 : 3319081535
Total Pages : 153 pages
Book Rating : 4.33/5 ( download)

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Download or read book Algebraic K-theory of Crystallographic Groups written by Daniel Scott Farley and published by Springer. This book was released on 2014-08-27 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Vasudevan Srinivas
Publisher : Springer Science & Business Media
ISBN 13 : 0817647392
Total Pages : 357 pages
Book Rating : 4.91/5 ( download)

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Download or read book Algebraic K-Theory written by Vasudevan Srinivas and published by Springer Science & Business Media. This book was released on 2009-05-21 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 students in mathematics. This book is based on lectures given by the author at the Tata Institute in Bombay and elsewhere. This new edition includes an appendix on algebraic geometry that contains required definitions and results needed to understand the core of the book.

Author : Bjørn Ian Dundas
Publisher : Springer Science & Business Media
ISBN 13 : 1447143930
Total Pages : 447 pages
Book Rating : 4.32/5 ( download)

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Download or read book The Local Structure of Algebraic K-Theory written by Bjørn Ian Dundas and published by Springer Science & Business Media. This book was released on 2012-09-06 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Richard G. Swan
Publisher : Springer
ISBN 13 : 3540359176
Total Pages : 269 pages
Book Rating : 4.73/5 ( download)

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Download or read book Algebraic K-Theory written by Richard G. Swan and published by Springer. This book was released on 2006-11-14 with total page 269 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Wayne Raskind
Publisher : American Mathematical Soc.
ISBN 13 : 082180927X
Total Pages : 330 pages
Book Rating : 4.73/5 ( download)

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Download or read book Algebraic $K$-Theory written by Wayne Raskind and published by American Mathematical Soc.. This book was released on 1999 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Hyman Bass
Publisher : World Scientific
ISBN 13 : 9814544795
Total Pages : 622 pages
Book Rating : 4.95/5 ( download)

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Download or read book Algebraic K-theory And Its Applications - Proceedings Of The School written by Hyman Bass and published by World Scientific. This book was released on 1999-03-12 with total page 622 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Emilio Lluis-Puebla
Publisher : Springer
ISBN 13 : 3540466398
Total Pages : 172 pages
Book Rating : 4.90/5 ( download)

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Download or read book Higher Algebraic K-Theory: An Overview written by Emilio Lluis-Puebla and published by Springer. This book was released on 2006-11-14 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Robert M.F. Moss
Publisher : Springer
ISBN 13 : 3540361561
Total Pages : 95 pages
Book Rating : 4.65/5 ( download)

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Download or read book Algebraic K-Theory and its Geometric Applications written by Robert M.F. Moss and published by Springer. This book was released on 2006-11-15 with total page 95 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Jonathan Rosenberg
Publisher : Springer Science & Business Media
ISBN 13 : 1461243149
Total Pages : 404 pages
Book Rating : 4.44/5 ( download)

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Download or read book Algebraic K-Theory and Its Applications written by Jonathan Rosenberg and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Hvedri Inassaridze
Publisher : Springer Science & Business Media
ISBN 13 : 9401585695
Total Pages : 444 pages
Book Rating : 4.99/5 ( download)

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Download or read book Algebraic K-Theory written by Hvedri Inassaridze and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.