Cohomology And K Theory Of Discrete Groups
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Cohomology And K Theory Of Discrete Groups
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Author : Daniel Juan-Pineda
language : en
Publisher:
Release Date : 1994
Cohomology And K Theory Of Discrete Groups written by Daniel Juan-Pineda and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with categories.
The Local Structure Of Algebraic K Theory
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Author : Bjørn Ian Dundas
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-09-06
The Local Structure Of Algebraic K Theory written by Bjørn Ian Dundas and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-09-06 with Mathematics categories.
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.
Homology Of Linear Groups
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Author : Kevin P. Knudson
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Homology Of Linear Groups written by Kevin P. Knudson and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Daniel Quillen's definition of the higher algebraic K-groups of a ring emphasized the importance of computing the homology of groups of matrices. This text traces the development of this theory from Quillen's fundamental calculation. It presents the stability theorems and low-dimensional results of A. Suslin, W. van der Kallen and others are presented. Coverage also examines the Friedlander-Milnor-conjecture concerning the homology of algebraic groups made discrete.
General Cohomology Theory And K Theory
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Author : P. J. Hilton
language : en
Publisher: Cambridge University Press
Release Date : 1971-02-28
General Cohomology Theory And K Theory written by P. J. Hilton and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971-02-28 with Mathematics categories.
These notes constitute a faithful record of a short course of lectures given in São Paulo, Brazil, in the summer of 1968. The audience was assumed to be familiar with the basic material of homology and homotopy theory, and the object of the course was to explain the methodology of general cohomology theory and to give applications of K-theory to familiar problems such as that of the existence of real division algebras. The audience was not assumed to be sophisticated in homological algebra, so one chapter is devoted to an elementary exposition of exact couples and spectral sequences.
Cohomology Of Groups And Algebraic K Theory
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Author :
language : en
Publisher:
Release Date : 2009
Cohomology Of Groups And Algebraic K Theory written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Group theory categories.
Twisted Equivariant K Theory For Proper Actions Of Discrete Groups
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Author : Christopher Dwyer
language : en
Publisher:
Release Date : 2005
Twisted Equivariant K Theory For Proper Actions Of Discrete Groups written by Christopher Dwyer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with categories.
Algebraic K Theory Of Crystallographic Groups
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Author : Daniel Scott Farley
language : en
Publisher: Springer
Release Date : 2014-08-27
Algebraic K Theory Of Crystallographic Groups written by Daniel Scott Farley and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-27 with Mathematics categories.
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.
Algebraic K Theory Connections With Geometry And Topology
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Author : John Jardine
language : en
Publisher: Springer Science & Business Media
Release Date : 1989-06-30
Algebraic K Theory Connections With Geometry And Topology written by John Jardine and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-06-30 with Mathematics categories.
A NATO Advanced Study Institute entitled "Algebraic K-theory: Connections with Geometry and Topology" was held at the Chateau Lake Louise, Lake Louise, Alberta, Canada from December 7 to December 11 of 1987. This meeting was jointly supported by NATO and the Natural Sciences and Engineering Research Council of Canada, and was sponsored in part by the Canadian Mathematical Society. This book is the volume of proceedings for that meeting. Algebraic K-theory is essentially the study of homotopy invariants arising from rings and their associated matrix groups. More importantly perhaps, the subject has become central to the study of the relationship between Topology, Algebraic Geometry and Number Theory. It draws on all of these fields as a subject in its own right, but it serves as well as an effective translator for the application of concepts from one field in another. The papers in this volume are representative of the current state of the subject. They are, for the most part, research papers which are primarily of interest to researchers in the field and to those aspiring to be such. There is a section on problems in this volume which should be of particular interest to students; it contains a discussion of the problems from Gersten's well-known list of 1973, as well as a short list of new problems.
Topology And K Theory
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Author : Robert Penner
language : en
Publisher: Springer Nature
Release Date : 2020-04-25
Topology And K Theory written by Robert Penner and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-25 with Mathematics categories.
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 1979-1980. He had just received the Fields Medal for his work on these topics among others and was funny and playful with a confident humility from the start. These are not meant to be polished lecture notes, rather, things are presented as did Quillen reflected in the hand-written notes, resisting any temptation to change or add notation, details or elaborations. Indeed, the text is faithful to Quillen's own exposition, even respecting the {\sl board-like presentation} of formulae, diagrams and proofs, omitting numbering theorems in favor of names and so on. This is meant to be Quillen on Quillen as it happened forty years ago, an informal text for a second-semester graduate student on topology, category theory and K-theory, a potential preface to studying Quillen's own landmark papers and an informal glimpse of his great mind. The intellectual pace of the lectures, namely fast and lively, is Quillen himself, and part of the point here is to capture some of this intimacy. To be sure, much has happened since then from this categorical perspective started by Grothendieck, and Misha Kapranov has contributed an Afterword in order to make it more useful to current students.
Cohomology Of Finite Groups
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Author : Alejandro Adem
language : en
Publisher: Springer
Release Date : 1994-07-26
Cohomology Of Finite Groups written by Alejandro Adem and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-07-26 with Mathematics categories.
The cohomology of groups has, since its beginnings in the 1920s and 1930s, been the stage for significant interaction between algebra and topology and has led to the creation of important new fields in mathematics, like homological algebra and algebraic K-theory. This is the first book to deal comprehensively with the cohomology of finite groups: it introduces the most important and useful algebraic and topological techniques, and describes the interplay of the subject with those of homotopy theory, representation theory and group actions. The combination of theory and examples, together with the techniques for computing the cohomology of important classes of groups including symmetric groups, alternating groups, finite groups of Lie type, and some of the sporadic simple groups, enable readers to acquire an in-depth understanding of group cohomology and its extensive applications.