Cohomology Of Groups And Algebraic K Theory
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Cohomology of Groups and Algebraic K theory
Author | : Anonim |
Publsiher | : Unknown |
Total Pages | : 517 |
Release | : 2009 |
Genre | : Group theory |
ISBN | : 7040266261 |
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Cohomology of Groups and Algebraic K theory
Author | : Lizhen Ji,Kefeng Liu,Shing-Tung Yau |
Publsiher | : International Press of Boston |
Total Pages | : 0 |
Release | : 2010 |
Genre | : Cohomology operations |
ISBN | : 1571461442 |
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Cohomology of Groups and Algebraic K-theory --
The Local Structure of Algebraic K Theory
Author | : Bjørn Ian Dundas,Thomas G. Goodwillie,Randy McCarthy |
Publsiher | : Springer Science & Business Media |
Total Pages | : 447 |
Release | : 2012-09-06 |
Genre | : Mathematics |
ISBN | : 9781447143932 |
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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.
Algebraic K theory And Its Applications Proceedings Of The School
Author | : Hyman Bass,Aderemi Oluyomi Kuku,C Pedrini |
Publsiher | : World Scientific |
Total Pages | : 622 |
Release | : 1999-03-12 |
Genre | : Electronic Book |
ISBN | : 9789814544795 |
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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.
Algebraic K Theory
Author | : Vasudevan Srinivas |
Publsiher | : Springer Science & Business Media |
Total Pages | : 328 |
Release | : 2013-11-21 |
Genre | : Science |
ISBN | : 9781489967350 |
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Algebraic K Theory and Its Applications
Author | : Jonathan Rosenberg |
Publsiher | : Springer Science & Business Media |
Total Pages | : 404 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 9781461243144 |
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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.
Higher Algebraic K Theory An Overview
Author | : Emilio Lluis-Puebla,Jean-Louis Loday,Henri Gillet,Christophe Soule,Victor Snaith |
Publsiher | : Springer |
Total Pages | : 172 |
Release | : 2006-11-14 |
Genre | : Mathematics |
ISBN | : 9783540466390 |
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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.
Handbook of K Theory
Author | : Eric Friedlander,Daniel R. Grayson |
Publsiher | : Springer Science & Business Media |
Total Pages | : 1148 |
Release | : 2005-07-18 |
Genre | : Mathematics |
ISBN | : 9783540230199 |
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This handbook offers a compilation of techniques and results in K-theory. Each chapter is dedicated to a specific topic and is written by a leading expert. Many chapters present historical background; some present previously unpublished results, whereas some present the first expository account of a topic; many discuss future directions as well as open problems. It offers an exposition of our current state of knowledge as well as an implicit blueprint for future research.