Complex Topological K Theory
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Complex Topological K Theory
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Author : Efton Park
language : en
Publisher: Cambridge University Press
Release Date : 2008-03-13
Complex Topological K Theory written by Efton Park 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 2008-03-13 with Mathematics categories.
Topological K-theory is a key tool in topology, differential geometry and index theory, yet this is the first contemporary introduction for graduate students new to the subject. No background in algebraic topology is assumed; the reader need only have taken the standard first courses in real analysis, abstract algebra, and point-set topology. The book begins with a detailed discussion of vector bundles and related algebraic notions, followed by the definition of K-theory and proofs of the most important theorems in the subject, such as the Bott periodicity theorem and the Thom isomorphism theorem. The multiplicative structure of K-theory and the Adams operations are also discussed and the final chapter details the construction and computation of characteristic classes. With every important aspect of the topic covered, and exercises at the end of each chapter, this is the definitive book for a first course in topological K-theory.
Topics In Algebraic And Topological K Theory
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Author : Paul Frank Baum
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-11-05
Topics In Algebraic And Topological K Theory written by Paul Frank Baum 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 2010-11-05 with Mathematics categories.
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.
Algebraic K Theory And Algebraic Topology
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Author : P.G. Goerss
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Algebraic K Theory And Algebraic Topology written by P.G. Goerss 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 2013-04-17 with Mathematics categories.
A NATO Advanced Study Institute entitled "Algebraic K-theory and Algebraic Topology" was held at Chateau Lake Louise, Lake Louise, Alberta, Canada from December 12 to December 16 of 1991. This book is the volume of proceedings for this meeting. The papers that appear here are representative of most of the lectures that were given at the conference, and therefore present a "snapshot" of the state ofthe K-theoretic art at the end of 1991. The underlying objective of the meeting was to discuss recent work related to the Lichtenbaum-Quillen complex of conjectures, fro~ both the algebraic and topological points of view. The papers in this volume deal with a range of topics, including motivic cohomology theories, cyclic homology, intersection homology, higher class field theory, and the former telescope conjecture. This meeting was jointly funded by grants from NATO and the National Science Foun dation in the United States. I would like to take this opportunity to thank these agencies for their support. I would also like to thank the other members of the organizing com mittee, namely Paul Goerss, Bruno Kahn and Chuck Weibel, for their help in making the conference successful. This was the second NATO Advanced Study Institute to be held in this venue; the first was in 1987. The success of both conferences owes much to the professionalism and helpfulness of the administration and staff of Chateau Lake Louise.
Algebraic K Theory
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Author : Vasudevan Srinivas
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-21
Algebraic K Theory written by Vasudevan Srinivas 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 2013-11-21 with Science categories.
Some Applications Of Topological K Theory
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Author :
language : en
Publisher: Elsevier
Release Date : 1980-01-01
Some Applications Of Topological K Theory written by and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980-01-01 with Mathematics categories.
Some Applications of Topological K-Theory
Bulk And Boundary Invariants For Complex Topological Insulators
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Author : Emil Prodan
language : en
Publisher: Springer
Release Date : 2016-02-05
Bulk And Boundary Invariants For Complex Topological Insulators written by Emil Prodan and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-02-05 with Science categories.
This monograph offers an overview of rigorous results on fermionic topological insulators from the complex classes, namely, those without symmetries or with just a chiral symmetry. Particular focus is on the stability of the topological invariants in the presence of strong disorder, on the interplay between the bulk and boundary invariants and on their dependence on magnetic fields. The first part presents motivating examples and the conjectures put forward by the physics community, together with a brief review of the experimental achievements. The second part develops an operator algebraic approach for the study of disordered topological insulators. This leads naturally to the use of analytical tools from K-theory and non-commutative geometry, such as cyclic cohomology, quantized calculus with Fredholm modules and index pairings. New results include a generalized Streda formula and a proof of the delocalized nature of surface states in topological insulators with non-trivial invariants. The concluding chapter connects the invariants to measurable quantities and thus presents a refined physical characterization of the complex topological insulators. This book is intended for advanced students in mathematical physics and researchers alike.
Algebraic K Theory And Its Applications
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Author : Jonathan Rosenberg
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Algebraic K Theory And Its Applications written by Jonathan Rosenberg 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 2012-12-06 with Mathematics categories.
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.
K Theory
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Author : Max Karoubi
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-11-27
K Theory written by Max Karoubi 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 2009-11-27 with Mathematics categories.
From the Preface: K-theory was introduced by A. Grothendieck in his formulation of the Riemann- Roch theorem. For each projective algebraic variety, Grothendieck constructed a group from the category of coherent algebraic sheaves, and showed that it had many nice properties. Atiyah and Hirzebruch considered a topological analog defined for any compact space X, a group K{X) constructed from the category of vector bundles on X. It is this ''topological K-theory" that this book will study. Topological K-theory has become an important tool in topology. Using K- theory, Adams and Atiyah were able to give a simple proof that the only spheres which can be provided with H-space structures are S1, S3 and S7. Moreover, it is possible to derive a substantial part of stable homotopy theory from K-theory. The purpose of this book is to provide advanced students and mathematicians in other fields with the fundamental material in this subject. In addition, several applications of the type described above are included. In general we have tried to make this book self-contained, beginning with elementary concepts wherever possible; however, we assume that the reader is familiar with the basic definitions of homotopy theory: homotopy classes of maps and homotopy groups.Thus this book might be regarded as a fairly self-contained introduction to a "generalized cohomology theory".
K Theory
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Author : Michael Atiyah
language : en
Publisher: CRC Press
Release Date : 2018-03-05
K Theory written by Michael Atiyah and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-05 with Mathematics categories.
These notes are based on the course of lectures I gave at Harvard in the fall of 1964. They constitute a self-contained account of vector bundles and K-theory assuming only the rudiments of point-set topology and linear algebra. One of the features of the treatment is that no use is made of ordinary homology or cohomology theory. In fact, rational cohomology is defined in terms of K-theory.The theory is taken as far as the solution of the Hopf invariant problem and a start is mode on the J-homomorphism. In addition to the lecture notes proper, two papers of mine published since 1964 have been reproduced at the end. The first, dealing with operations, is a natural supplement to the material in Chapter III. It provides an alternative approach to operations which is less slick but more fundamental than the Grothendieck method of Chapter III, and it relates operations and filtration. Actually, the lectures deal with compact spaces, not cell-complexes, and so the skeleton-filtration does not figure in the notes. The second paper provides a new approach to K-theory and so fills an obvious gap in the lecture notes.
Algebraic K Theory Connections With Geometry And Topology
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Author : John F. Jardine
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Algebraic K Theory Connections With Geometry And Topology written by John F. 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 2012-12-06 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.