Rational Homotopy Theory and Differential Forms
Rational Homotopy Theory and Differential Forms

Author: Phillip Griffiths

Publisher: Springer Science & Business Media

Published: 2013-10-02

Total Pages: 228

ISBN-13: 1461484685

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This completely revised and corrected version of the well-known Florence notes circulated by the authors together with E. Friedlander examines basic topology, emphasizing homotopy theory. Included is a discussion of Postnikov towers and rational homotopy theory. This is then followed by an in-depth look at differential forms and de Tham’s theorem on simplicial complexes. In addition, Sullivan’s results on computing the rational homotopy type from forms is presented. New to the Second Edition: *Fully-revised appendices including an expanded discussion of the Hirsch lemma *Presentation of a natural proof of a Serre spectral sequence result *Updated content throughout the book, reflecting advances in the area of homotopy theory With its modern approach and timely revisions, this second edition of Rational Homotopy Theory and Differential Forms will be a valuable resource for graduate students and researchers in algebraic topology, differential forms, and homotopy theory.

Rational Homotopy Theory and Differential Forms
Rational Homotopy Theory and Differential Forms

Author: Phillip Griffiths

Publisher: Birkhäuser

Published: 2013-10-02

Total Pages: 0

ISBN-13: 9781461484677

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This completely revised and corrected version of the well-known Florence notes circulated by the authors together with E. Friedlander examines basic topology, emphasizing homotopy theory. Included is a discussion of Postnikov towers and rational homotopy theory. This is then followed by an in-depth look at differential forms and de Tham’s theorem on simplicial complexes. In addition, Sullivan’s results on computing the rational homotopy type from forms is presented. New to the Second Edition: *Fully-revised appendices including an expanded discussion of the Hirsch lemma *Presentation of a natural proof of a Serre spectral sequence result *Updated content throughout the book, reflecting advances in the area of homotopy theory With its modern approach and timely revisions, this second edition of Rational Homotopy Theory and Differential Forms will be a valuable resource for graduate students and researchers in algebraic topology, differential forms, and homotopy theory.

Differential Forms in Algebraic Topology
Differential Forms in Algebraic Topology

Author: Raoul Bott

Publisher: Springer Science & Business Media

Published: 2013-04-17

Total Pages: 319

ISBN-13: 1475739516

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Developed from a first-year graduate course in algebraic topology, this text is an informal introduction to some of the main ideas of contemporary homotopy and cohomology theory. The materials are structured around four core areas: de Rham theory, the Cech-de Rham complex, spectral sequences, and characteristic classes. By using the de Rham theory of differential forms as a prototype of cohomology, the machineries of algebraic topology are made easier to assimilate. With its stress on concreteness, motivation, and readability, this book is equally suitable for self-study and as a one-semester course in topology.

Cohomology and Differential Forms
Cohomology and Differential Forms

Author: Izu Vaisman

Publisher: Courier Dover Publications

Published: 2016-08-17

Total Pages: 305

ISBN-13: 0486804836

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This monograph explores the cohomological theory of manifolds with various sheaves and its application to differential geometry. Based on lectures given by author Izu Vaisman at Romania's University of Iasi, the treatment is suitable for advanced undergraduates and graduate students of mathematics as well as mathematical researchers in differential geometry, global analysis, and topology. A self-contained development of cohomological theory constitutes the central part of the book. Topics include categories and functors, the Čech cohomology with coefficients in sheaves, the theory of fiber bundles, and differentiable, foliated, and complex analytic manifolds. The final chapter covers the theorems of de Rham and Dolbeault-Serre and examines the theorem of Allendoerfer and Eells, with applications of these theorems to characteristic classes and the general theory of harmonic forms.

Cohomology Operations and Applications in Homotopy Theory
Cohomology Operations and Applications in Homotopy Theory

Author: Robert E. Mosher

Publisher: Courier Corporation

Published: 2008-01-01

Total Pages: 226

ISBN-13: 0486466647

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Cohomology operations are at the center of a major area of activity in algebraic topology. This treatment explores the single most important variety of operations, the Steenrod squares. It constructs these operations, proves their major properties, and provides numerous applications, including several different techniques of homotopy theory useful for computation. 1968 edition.

Introduction to Differential Topology
Introduction to Differential Topology

Author: Theodor Bröcker

Publisher: Cambridge University Press

Published: 1982-09-16

Total Pages: 176

ISBN-13: 9780521284707

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This book is intended as an elementary introduction to differential manifolds. The authors concentrate on the intuitive geometric aspects and explain not only the basic properties but also teach how to do the basic geometrical constructions. An integral part of the work are the many diagrams which illustrate the proofs. The text is liberally supplied with exercises and will be welcomed by students with some basic knowledge of analysis and topology.

Differential Topology
Differential Topology

Author: Morris W. Hirsch

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 230

ISBN-13: 146849449X

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"A very valuable book. In little over 200 pages, it presents a well-organized and surprisingly comprehensive treatment of most of the basic material in differential topology, as far as is accessible without the methods of algebraic topology....There is an abundance of exercises, which supply many beautiful examples and much interesting additional information, and help the reader to become thoroughly familiar with the material of the main text." —MATHEMATICAL REVIEWS

A Geometric Approach to Differential Forms
A Geometric Approach to Differential Forms

Author: David Bachman

Publisher: Springer Science & Business Media

Published: 2012-02-02

Total Pages: 167

ISBN-13: 0817683046

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This text presents differential forms from a geometric perspective accessible at the undergraduate level. It begins with basic concepts such as partial differentiation and multiple integration and gently develops the entire machinery of differential forms. The subject is approached with the idea that complex concepts can be built up by analogy from simpler cases, which, being inherently geometric, often can be best understood visually. Each new concept is presented with a natural picture that students can easily grasp. Algebraic properties then follow. The book contains excellent motivation, numerous illustrations and solutions to selected problems.

Rational Homotopy Theory
Rational Homotopy Theory

Author: Yves Felix

Publisher: Springer Science & Business Media

Published: 2001

Total Pages: 589

ISBN-13: 0387950680

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This is a long awaited book on rational homotopy theory which contains all the main theorems with complete proofs, and more elementary proofs for many results that were proved ten or fifteen years ago. The authors added a frist section on classical algebraic topology to make the book accessible to students with only little background in algebraic topology.