By Jean Dieudonné

Since the early a part of the twentieth century, topology has steadily unfold to many different branches of arithmetic, and this ebook demonstrates how the topic maintains to play a relevant function within the box. Written by way of a world-renowned mathematician, this vintage textual content strains the historical past of algebraic topology starting with its construction within the early 1900s and describes intimately the real theories that have been came across prior to 1960. throughout the paintings of Poincaré, de Rham, Cartan, Hureqicz, etc, this historic e-book additionally specializes in the emergence of recent principles and techniques that experience led 21st-century mathematicians in the direction of new learn directions.

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This e-book is a well-informed and particular research of the issues and improvement of algebraic topology, from Poincaré and Brouwer to Serre, Adams, and Thom. the writer has tested every one major paper alongside this course and describes the stairs and technique of its proofs and its relation to different paintings. formerly, the background of the various technical advancements of 20th-century arithmetic had looked as if it would current insuperable hindrances to scholarship. This publication demonstrates in terms of topology how those hindrances might be triumph over, with enlightening results.... inside its selected limitations the assurance of this e-book is excellent. learn it!

—MathSciNet

[The writer] lines the advance of algebraic and differential topology from the leading edge paintings through Poincaré on the flip of the century to the interval round 1960. [He] has given an outstanding account of the expansion of those fields.… the main points are interwoven with the narrative in a truly friendly fashion.… [The writer] has past written histories of useful research and of algebraic geometry, yet neither e-book was once on this type of grand scale as this one. He has made it attainable to track the $64000 steps within the progress of algebraic and differential topology, and to recognize the exertions and significant advances made through the founders.

—Zentralblatt MATH

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1007/978-0-8176-4907-4_2, © Birkhäuser Boston, a part of Springer Science+Business Media, LLC 2009 J.

J. 1007/978-0-8176-4907-4_2, © Birkhäuser Boston, a part of Springer Science+Business Media, LLC 2009 J.

1007/978-0-8176-4907-4_2, © Birkhäuser Boston, a part of Springer Science+Business Media, LLC 2009 J.

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