A History of Algebraic and Differential Topology, 1900-1960

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9780817649067: A History of Algebraic and Differential Topology, 1900-1960

This book is a well-informed and detailed analysis of the problems and development of algebraic topology, from Poincare and Brouwer to Serre, Adams, and Thom. The author has examined each significant paper along this route and describes the steps and strategy of its proofs and its relation to other work. Previously, the history of the many technical developments of 20th-century mathematics had seemed to present insuperable obstacles to scholarship. This book demonstrates in the case of topology how these obstacles can be overcome, with enlightening results...Within its chosen boundaries the coverage of this book is superb. Read it! -MathSciNet

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Dalla quarta di copertina:

Since the early part of the 20th century, topology has gradually spread to many other branches of mathematics, and this book demonstrates how the subject continues to play a central role in the field. Written by a world-renowned mathematician, this classic text traces the history of algebraic topology beginning with its creation in the early 1900s and describes in detail the important theories that were discovered before 1960. Through the work of Poincaré, de Rham, Cartan, Hureqicz, and many others, this historical book also focuses on the emergence of new ideas and methods that have led 21st-century mathematicians towards new research directions.

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This book is a well-informed and detailed analysis of the problems and development of algebraic topology, from Poincaré and Brouwer to Serre, Adams, and Thom. The author has examined each significant paper along this route and describes the steps and strategy of its proofs and its relation to other work. Previously, the history of the many technical developments of 20th-century mathematics had seemed to present insuperable obstacles to scholarship. This book demonstrates in the case of topology how these obstacles can be overcome, with enlightening results.... Within its chosen boundaries the coverage of this book is superb. Read it!

—MathSciNet

[The author] traces the development of algebraic and differential topology from the innovative work by Poincaré at the turn of the century to the period around 1960. [He] has given a superb account of the growth of these fields.… The details are interwoven with the narrative in a very pleasant fashion.… [The author] has previous written histories of functional analysis and of algebraic geometry, but neither book was on such a grand scale as this one. He has made it possible to trace the important steps in the growth of algebraic and differential topology, and to admire the hard work and major advances made by the founders.

—Zentralblatt MATH

Contenuti:

Preface.- Notations.- Part 1. Simplicial Techniques and Homology.- Introduction.- The Work of Poincaré.- The Build-Up of 'Classical' Homology.- The Beginnings of Differential Topology.- The Various Homology and Cohomology Theories.- Part 2. The First Applications of Simplicial Methods and of Homology.- Introduction.- The Concept of Degree.- Dimension Theory and Separation Theorems.- Fixed Points.- Local Homological Properties.- Quotient Spaces and Their Homology.- Homology of Groups and Homogeneous Spaces.- Applications of Homology to Geometry and Analysis.- Part 3. Homotopy and its Relation to Homology.- Introduction.- Fundamental Group and Covering Spaces.- Elementary Notions and Early Results in Homotopy Theory.- Fibrations.- Homology of Fiberations.- Sophisticated Relations between Homotopy and Homology.- Cohomology Operations.- Generalized Homology and Cohomology.- Bibliography.- Index of Cited Names.- Subject Index.

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Jean A. Dieudonne
Editore: BIRKHAUSER BOSTON INC, United States (2009)
ISBN 10: 0817649069 ISBN 13: 9780817649067
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Descrizione libro BIRKHAUSER BOSTON INC, United States, 2009. Paperback. Condizione libro: New. 229 x 155 mm. Language: English Brand New Book ***** Print on Demand *****.This book is a well-informed and detailed analysis of the problems and development of algebraic topology, from Poincare and Brouwer to Serre, Adams, and Thom. The author has examined each significant paper along this route and describes the steps and strategy of its proofs and its relation to other work. Previously, the history of the many technical developments of 20th-century mathematics had seemed to present insuperable obstacles to scholarship. This book demonstrates in the case of topology how these obstacles can be overcome, with enlightening results.Within its chosen boundaries the coverage of this book is superb. Read it! -MathSciNet 1st ed. 1989. Softcover printing of hardcover edition. 2009. Codice libro della libreria AAV9780817649067

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Jean A. Dieudonne
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Descrizione libro BIRKHAUSER BOSTON INC, United States, 2009. Paperback. Condizione libro: New. 229 x 155 mm. Language: English . Brand New Book ***** Print on Demand *****. This book is a well-informed and detailed analysis of the problems and development of algebraic topology, from Poincare and Brouwer to Serre, Adams, and Thom. The author has examined each significant paper along this route and describes the steps and strategy of its proofs and its relation to other work. Previously, the history of the many technical developments of 20th-century mathematics had seemed to present insuperable obstacles to scholarship. This book demonstrates in the case of topology how these obstacles can be overcome, with enlightening results.Within its chosen boundaries the coverage of this book is superb. Read it! -MathSciNet 1st ed. 1989. Softcover printing of hardcover edition. 2009. Codice libro della libreria AAV9780817649067

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