Differential Geometry

A History of Algebraic and Differential Topology, 1900 - by Jean Dieudonné

By Jean Dieudonné

Since the early a part of the 20 th century, topology has progressively unfold to many different branches of arithmetic, and this publication demonstrates how the topic maintains to play a important function within the box. Written by way of a world-renowned mathematician, this vintage textual content strains the heritage of algebraic topology starting with its production within the early 1900s and describes intimately the real theories that have been found earlier than 1960. throughout the paintings of Poincaré, de Rham, Cartan, Hureqicz, etc, this old ebook additionally makes a speciality of the emergence of latest principles and strategies that experience led 21st-century mathematicians in the direction of new study directions.

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This publication is a well-informed and unique 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 numerous technical advancements of 20th-century arithmetic had looked as if it would current insuperable stumbling blocks to scholarship. This ebook demonstrates with regards to topology how those stumbling blocks will be triumph over, with enlightening results.... inside of its selected limitations the assurance of this booklet is excellent. learn it!

—MathSciNet

[The writer] lines the advance of algebraic and differential topology from the leading edge paintings by way of Poincaré on the flip of the century to the interval round 1960. [He] has given a great account of the expansion of those fields.… the main points are interwoven with the narrative in a really friendly fashion.… [The writer] has earlier written histories of practical research and of algebraic geometry, yet neither ebook used to be on this sort of grand scale as this one. He has made it attainable to track the real steps within the development of algebraic and differential topology, and to appreciate the labor and significant advances made via 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.

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.

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