K-theory

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Author: Michael Atiyah

Publisher: CRC Press

ISBN: 0429973179

Category: Mathematics

Page: 240

View: 7904

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.

The $K$-book

An Introduction to Algebraic $K$-theory

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Author: Charles A. Weibel

Publisher: American Mathematical Soc.

ISBN: 0821891324

Category: Mathematics

Page: 618

View: 377

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

Algebraic K-Theory

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Author: V. Srinivas

Publisher: Springer Science & Business Media

ISBN: 0817647368

Category: Mathematics

Page: 341

View: 4445

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 graduate students in mathematics. The book is based on lectures given at the author's home institution, the Tata Institute in Bombay, and elsewhere. A detailed appendix on topology was provided in the first edition to make the treatment accessible to readers with a limited background in topology. The second edition also includes an appendix on algebraic geometry that contains the required definitions and results needed to understand the core of the book; this makes the book accessible to a wider audience. A central part of the book is a detailed exposition of the ideas of Quillen as contained in his classic papers "Higher Algebraic K-Theory, I, II." A more elementary proof of the theorem of Merkujev--Suslin is given in this edition; this makes the treatment of this topic self-contained. An application is also given to modules of finite length and finite projective dimension over the local ring of a normal surface singularity. These results lead the reader to some interesting conclusions regarding the Chow group of varieties. "It is a pleasure to read this mathematically beautiful book..." ---WW.J. Julsbergen, Mathematics Abstracts "The book does an admirable job of presenting the details of Quillen's work..." ---Mathematical Reviews

K-Theory

An Introduction

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Author: Max Karoubi

Publisher: Springer Science & Business Media

ISBN: 3540798900

Category: Mathematics

Page: 316

View: 9868

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".

Algebraic K-Theory and Its Applications

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Author: Jonathan Rosenberg

Publisher: Springer Science & Business Media

ISBN: 1461243149

Category: Mathematics

Page: 394

View: 9198

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.

An Algebraic Introduction to K-Theory

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Author: Bruce A. Magurn

Publisher: Cambridge University Press

ISBN: 9780521800785

Category: Mathematics

Page: 676

View: 1051

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

Modern Classical Homotopy Theory

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Author: Jeffrey Strom

Publisher: American Mathematical Soc.

ISBN: 0821852868

Category: Mathematics

Page: 835

View: 9847

The core of classical homotopy theory is a body of ideas and theorems that emerged in the 1950s and was later largely codified in the notion of a model category. This core includes the notions of fibration and cofibration; CW complexes; long fiber and cofiber sequences; loop spaces and suspensions; and so on. Brown's representability theorems show that homology and cohomology are also contained in classical homotopy theory. This text develops classical homotopy theory from a modern point of view, meaning that the exposition is informed by the theory of model categories and that homotopy limits and colimits play central roles. The exposition is guided by the principle that it is generally preferable to prove topological results using topology (rather than algebra). The language and basic theory of homotopy limits and colimits make it possible to penetrate deep into the subject with just the rudiments of algebra. The text does reach advanced territory, including the Steenrod algebra, Bott periodicity, localization, the Exponent Theorem of Cohen, Moore, and Neisendorfer, and Miller's Theorem on the Sullivan Conjecture. Thus the reader is given the tools needed to understand and participate in research at (part of) the current frontier of homotopy theory. Proofs are not provided outright. Rather, they are presented in the form of directed problem sets. To the expert, these read as terse proofs; to novices they are challenges that draw them in and help them to thoroughly understand the arguments.

K-theory

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Author: Michael Atiyah

Publisher: CRC Press

ISBN: 0429973179

Category: Mathematics

Page: 240

View: 8882

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.

Quantum Many-particle Systems

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Author: John W. Negele

Publisher: CRC Press

ISBN: 0429966474

Category: Science

Page: 476

View: 3947

This book explains the fundamental concepts and theoretical techniques used to understand the properties of quantum systems having large numbers of degrees of freedom. A number of complimentary approaches are developed, including perturbation theory; nonperturbative approximations based on functional integrals; general arguments based on order parameters, symmetry, and Fermi liquid theory; and stochastic methods.

Theory for Classics

A Student's Guide

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Author: Louise Hitchcock

Publisher: Taylor & Francis

ISBN: 0415454972

Category: History

Page: 213

View: 5726

This student's guide is a clear and concise handbook to the key connections between Classical Studies and critical theory in the twentieth century. Louise Hitchcock looks at the way Classics has been engaged across a number of disciplines. Beginning with four foundational figures - Freud, Marx, Nietzshe and Saussure - Hitchcock goes on to provide guided introductions of the major theoretical thinkers of the past century, from Adorno to Williams. Each entry offers biographical, theoretical and bibliographical information along with a discussion of each figure's relevance to Classical Studies and suggestions for future research. Theory for Classics, adapted from Theory for Religious Studies, by William E. Deal and Timothy K. Beal, is a brisk, thoughtful, provocative, and engaging title, which will be an essential first volume for anyone interested in the intersection between theory and classical studies today.

Quantum Electrodynamics

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Author: Richard P. Feynman

Publisher: CRC Press

ISBN: 0429972873

Category: Science

Page: 212

View: 6322

This classic work presents the main results and calculational procedures of quantum electrodynamics in a simple and straightforward way. Designed for the student of experimental physics who does not intend to take more advanced graduate courses in theoretical physics, the material consists of notes on the third of a three-semester course given at the California Institute of Technology.

Chronoschisms

Time, Narrative, and Postmodernism

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Author: Ursula K. Heise

Publisher: Cambridge University Press

ISBN: 9780521555449

Category: Literary Criticism

Page: 286

View: 9697

An analysis of the way postmodern novels respond to changes in the experience of time.

Complex Topological K-Theory

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Author: Efton Park

Publisher: Cambridge University Press

ISBN: 1139469746

Category: Mathematics

Page: N.A

View: 1744

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.

Theory of Literature and Other Critical Writings

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Author: Sōseki Natsume,Michael K. Bourdaghs,Atsuko Ueda

Publisher: Columbia University Press

ISBN: 9780231146562

Category: Literary Collections

Page: 287

View: 3644

"The Theory of Literature foreshadows the ideas and concepts that would later form the critical foundations of formalism, structuralism, reader-response theory, cognitive science, and postcolonialism. It remains an unprecedented work of literary theory, unmistakably modern yet also clearly (and self-consciously) non-Western. In a later series of lectures and essays, Soseki continued to develop his ideas. This material, some of it never before translated into English, is also included in the volume. The editors offer a critical introduction that contextualizes Soseki's theoretical project historically and explores its contemporary legacy."--BOOK JACKET.

Simplicial Homotopy Theory

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Author: Paul G. Goerss,John F. Jardine

Publisher: Birkhäuser

ISBN: 3034887078

Category: Mathematics

Page: 510

View: 9990

Einstein's Theory of Relativity

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Author: Max Born

Publisher: Courier Corporation

ISBN: 0486142124

Category: Science

Page: 400

View: 5504

Semi-technical account includes a review of classical physics (origin of space and time measurements, Ptolemaic and Copernican astronomy, laws of motion, inertia, more) and of Einstein's theories of relativity.

Characteristic Classes. (AM-76)

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Author: John Milnor,James D. Stasheff

Publisher: Princeton University Press

ISBN: 140088182X

Category: Mathematics

Page: 340

View: 958

The theory of characteristic classes provides a meeting ground for the various disciplines of differential topology, differential and algebraic geometry, cohomology, and fiber bundle theory. As such, it is a fundamental and an essential tool in the study of differentiable manifolds. In this volume, the authors provide a thorough introduction to characteristic classes, with detailed studies of Stiefel-Whitney classes, Chern classes, Pontrjagin classes, and the Euler class. Three appendices cover the basics of cohomology theory and the differential forms approach to characteristic classes, and provide an account of Bernoulli numbers. Based on lecture notes of John Milnor, which first appeared at Princeton University in 1957 and have been widely studied by graduate students of topology ever since, this published version has been completely revised and corrected.

Advanced Theory and Practice in Sport Marketing

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Author: Eric C. Schwarz,Jason D. Hunter

Publisher: Routledge

ISBN: 1351667629

Category: Business & Economics

Page: 380

View: 8407

Effective marketing is essential for any successful sport organization, from elite international teams to local leagues. Now in a fully revised and updated third edition, Advanced Theory and Practice in Sport Marketing is still the only text to introduce key theory and best practice at an advanced level. This new edition goes beyond the introductory marketing course by exploring advanced marketing theories related to social responsibility, global issues, information systems, consumer behavior, product management, logistics, sales, promotions, and social/digital/mobile media. New to the edition are sections on branding, destination marketing, and performance evaluation that demonstrate how to measure impacts through sport marketing and how to use analytics to determine sport marketing success. Every chapter contains extended case studies and theory-to-practice insights from marketing professionals around the world and a companion website includes an impressive array of additional teaching and learning resources. Advanced Theory and Practice in Sport Marketing goes further than any other textbook to prepare students for the real world of sport marketing. It is essential reading for any upper-level undergraduate or postgraduate course in sport marketing or sport business.

Theory of Mind and Literature

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Author: Paula Leverage

Publisher: Purdue University Press

ISBN: 1557535701

Category: Literary Criticism

Page: 329

View: 9058

Theory of Mind is what enables us to “put ourselves in another’s shoes.” It is mindreading, empathy, creative imagination of another’s perspective: in short, it is simultaneously a highly sophisticated ability and a very basic necessity for human communication. Theory of Mind is central to such commercial endeavors as market research and product development, but it is also just as important in maintaining human relations over a cup of coffee. Not surprisingly, it is a critical tool in reading and understanding literature, which abounds with characters, situations, and “other people’s shoes.” Furthermore, it is becoming increasingly apparent that reading literature also hones these critical mindreading skills. Theory of Mind and Literature is a collection of nineteen essays by prominent scholars (linguists, cognitive scientists, and philosophers) working in the cutting-edge field of cognitive literary studies, which explores how we use Theory of Mind in reading and understanding literature.