Author: Michael Atiyah

Publisher: CRC Press

ISBN: 0429973179

Category: Mathematics

Page: 240

View: 9149

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.

Global Differential Geometry


Author: Christian Bär,Joachim Lohkamp,Matthias Schwarz

Publisher: Springer Science & Business Media

ISBN: 3642228429

Category: Mathematics

Page: 524

View: 9700

This volume contains a collection of well-written surveys provided by experts in Global Differential Geometry to give an overview over recent developments in Riemannian Geometry, Geometric Analysis and Symplectic Geometry. The papers are written for graduate students and researchers with a general interest in geometry, who want to get acquainted with the current trends in these central fields of modern mathematics.


An Introduction


Author: Max Karoubi

Publisher: Springer Science & Business Media

ISBN: 3540798900

Category: Mathematics

Page: 316

View: 2348

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


Author: Vasudevan Srinivas

Publisher: Springer Science & Business Media

ISBN: 0817647368

Category: Mathematics

Page: 341

View: 5658

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.

Transformation Groups and Algebraic K-Theory


Author: Wolfgang Lück

Publisher: Springer

ISBN: 3540468277

Category: Mathematics

Page: 454

View: 5661

The book focuses on the relation between transformation groups and algebraic K-theory. The general pattern is to assign to a geometric problem an invariant in an algebraic K-group which determines the problem. The algebraic K-theory of modules over a category is studied extensively and appplied to the fundamental category of G-space. Basic details of the theory of transformation groups sometimes hard to find in the literature, are collected here (Chapter I) for the benefit of graduate students. Chapters II and III contain advanced new material of interest to researchers working in transformation groups, algebraic K-theory or related fields.

Advanced Integration Theory


Author: Corneliu Constantinescu,Wolfgang Filter,Karl Weber

Publisher: Springer Science & Business Media

ISBN: 9400708521

Category: Mathematics

Page: 876

View: 7778

Since about 1915 integration theory has consisted of two separate branches: the abstract theory required by probabilists and the theory, preferred by analysts, that combines integration and topology. As long as the underlying topological space is reasonably nice (e.g., locally compact with countable basis) the abstract theory and the topological theory yield the same results, but for more compli cated spaces the topological theory gives stronger results than those provided by the abstract theory. The possibility of resolving this split fascinated us, and it was one of the reasons for writing this book. The unification of the abstract theory and the topological theory is achieved by using new definitions in the abstract theory. The integral in this book is de fined in such a way that it coincides in the case of Radon measures on Hausdorff spaces with the usual definition in the literature. As a consequence, our integral can differ in the classical case. Our integral, however, is more inclusive. It was defined in the book "C. Constantinescu and K. Weber (in collaboration with A.

Using the Mathematics Literature


Author: Kristine K. Fowler

Publisher: CRC Press

ISBN: 9780824750350

Category: Language Arts & Disciplines

Page: 475

View: 9200

This reference serves as a reader-friendly guide to every basic tool and skill required in the mathematical library and helps mathematicians find resources in any format in the mathematics literature. It lists a wide range of standard texts, journals, review articles, newsgroups, and Internet and database tools for every major subfield in mathematics and details methods of access to primary literature sources of new research, applications, results, and techniques. Using the Mathematics Literature is the most comprehensive and up-to-date resource on mathematics literature in both print and electronic formats, presenting time-saving strategies for retrieval of the latest information.

Political Theory, Science Fiction, and Utopian Literature

Ursula K. Le Guin and The Dispossessed


Author: Tony Burns

Publisher: Lexington Books

ISBN: 0739122827

Category: Literary Criticism

Page: 319

View: 6908

This work challenges both the widely accepted view thatThe Dispossessed represents a new kind of literary utopia and the place of Ursula K. Le Guin's novel in the histories of utopian/dystopian literature and science fiction.

Ethics, Literature, and Theory

An Introductory Reader


Author: Stephen K. George

Publisher: Rowman & Littlefield

ISBN: 9780742532342

Category: Literary Criticism

Page: 401

View: 2823

Do the rich descriptions and narrative shapings of literature provide a valuable resource for readers, writers, philosophers, and everyday people to imagine and confront the ultimate questions of life? Do the human activities of storytelling and complex moral decision-making have a deep connection? What are the moral responsibilities of the artist, critic, and reader? What can religious perspectives—from Catholic to Protestant to Mormon—contribute to literary criticism? Thirty well known contributors reflect on these questions, including iterary theorists Marshall Gregory, James Phelan, and Wayne Booth; philosophers Martha Nussbaum, Richard Hart, and Nina Rosenstand; and authors John Updike, Charles Johnson, Flannery O'Connor, and Bernard Malamud. Divided into four sections, with introductory matter and questions for discussion, this accessible anthology represents the most crucial work today exploring the interdisciplinary connections between literature, religion and philosophy.

Basic Notions of Algebra


Author: Igor R. Shafarevich

Publisher: Springer Science & Business Media

ISBN: 9783540251774

Category: Mathematics

Page: 260

View: 8129

Wholeheartedly recommended to every student and user of mathematics, this is an extremely original and highly informative essay on algebra and its place in modern mathematics and science. From the fields studied in every university maths course, through Lie groups to cohomology and category theory, the author shows how the origins of each concept can be related to attempts to model phenomena in physics or in other branches of mathematics. Required reading for mathematicians, from beginners to experts.

Curriculum Integration K-12

Theory and Practice


Author: James S. Etim

Publisher: University Press of America

ISBN: 9780761828983

Category: Education

Page: 207

View: 4645

Following the pioneering work of James Beane and Heidi Jacobs, there is now a growing interest in the area of integrative teaching. Contributors to this edited volume include K-12 principals and teachers as well as university professors recently involved in the implementation of integrative teaching.

Simplicial Homotopy Theory


Author: Paul G. Goerss,John F. Jardine

Publisher: Birkhäuser

ISBN: 3034887078

Category: Mathematics

Page: 510

View: 4747

Since the beginning of the modern era of algebraic topology, simplicial methods have been used systematically and effectively for both computation and basic theory. With the development of Quillen's concept of a closed model category and, in particular, a simplicial model category, this collection of methods has become the primary way to describe non-abelian homological algebra and to address homotopy-theoretical issues in a variety of fields, including algebraic K-theory. This book supplies a modern exposition of these ideas, emphasizing model category theoretical techniques. Discussed here are the homotopy theory of simplicial sets, and other basic topics such as simplicial groups, Postnikov towers, and bisimplicial sets. The more advanced material includes homotopy limits and colimits, localization with respect to a map and with respect to a homology theory, cosimplicial spaces, and homotopy coherence. Interspersed throughout are many results and ideas well-known to experts, but uncollected in the literature. Intended for second-year graduate students and beyond, this book introduces many of the basic tools of modern homotopy theory. An extensive background in topology is not assumed.

Theory of Literature and Other Critical Writings


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

Publisher: Columbia University Press

ISBN: 9780231146562

Category: Literary Collections

Page: 287

View: 1822

"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.

Theory Of Superconductivity


Author: J. Robert Schrieffer

Publisher: Grove/Atlantic, Inc.

ISBN: 9780738201207

Category: Science

Page: 332

View: 3230

A classic treatment of the field of superconductivity, with original formulas and techniques by a leading theorist in the field.

The classical commentary [electronic resource]

histories, practices, theory


Author: Roy K. Gibson,Christina Shuttleworth Kraus

Publisher: BRILL

ISBN: 9789004121539

Category: Literary Criticism

Page: 427

View: 2878

Written primarily by practising commentators, these papers examine the issues raised by the writing and reading of commentaries on classical Greek and Latin texts.


eine Vorlesungsmitschrift ; mit 6 Tabellen


Author: Richard Phillips Feynman

Publisher: De Gruyter Oldenbourg

ISBN: 9783486243376


Page: 208

View: 686

Die Quantenelektrodynamik (QED) beschreibt die Wechselwirkung von Licht und Materie, genauer: die Wechselwirkung von Elektronen, Positronen und Photonen. Mittlerweile ist diese Theorie schon älter als ein halbes Jahrhundert. Im Laufe der Jahre ist sie in vielen Energiebereichen getestet worden, nicht zuletzt mit Hilfe der modernen Teilchenbeschleuniger. Um so überraschender ist die Tatsache, daß man bis heute keinerlei Abweichungen zwischen den theoretischen Voraussagen und den experimentellen Daten gefunden hat! Die QED zählt damit zu den genauesten aller Theorien. Dieses Werk führt in die wichtigsten Ergebnisse und Rechenverfahren der Quantenelektrodynamik ein. Aus erster Hand wird der Leser auch mit den berühmten "Feynman-Graphen" vertraut gemacht.

Deconstruction and Critical Theory


Author: Peter V. Zima

Publisher: A&C Black

ISBN: 1847140386

Category: Philosophy

Page: 240

View: 5907

This book surveys the main schools and theorists of deconstruction, establishing their philosophical roots and tracing their intellectual development. It analyses their contribution to the understanding of literature and ideology, comparing their critical value and exploring the critical reaction to deconstruction and its limitations. The text is designed for students who wish to understand how and why deconstruction has become the dominant tool of the humanities. Deconstruction and Critical Theory marks a new stage in the reception history of Derrida's work and in the wider philosophical debate around deconstruction. Zima's study makes a strikingly original contribution to our better understanding of deconstruction and its various philosophic sources. Christopher Norris, University of Wales at Cardiff. Deconstruction And Critical Theory: surveys the main schools and theorists of deconstruction; establishes their philosophical roots; traces their intellectual development; analyses their contribution to the understanding of literature and ideology; compares their critical value; explores the critical reaction to deconstruction and its limitations. This is the ideal text for students who wish to understand how and why deconstruction has become the dominant tool of the Humanities.

Race, Culture, and Identity

Francophone West African and Caribbean Literature and Theory from Négritude to Créolité


Author: Shireen K. Lewis

Publisher: Lexington Books

ISBN: 9780739114735

Category: Social Science

Page: 166

View: 5263

In this groundbreaking book, Shireen Lewis gives a comprehensive analysis of the literary and theoretical discourse on race, culture, and identity by Francophone and Caribbean writers beginning in the early part of the twentieth century and continuing into the dawn of the new millennium. Examining the works of Patrick Chamoiseau, Raphaël Confiant, Aimé Césaire, Léopold Senghor, Léon Damas, and Paulette Nardal, Lewis traces a move away from the preoccupation with African origins and racial and cultural purity, toward concerns of hybridity and fragmentation in the New World or Diasporic space. In addition to exploring how this shift parallels the larger debate around modernism and postmodernism, Lewis makes a significant contribution by arguing for the inclusion of Martinican intellectual Paulette Nardal, and other women into the canon as significant contributors to the birth of modern black Francophone literature.