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Catalogue Information
Field name	Details
Dewey Class	510.9
Title	A History of Algebraic and Differential Topology, 1900 - 1960 ([Ebook]) / by Jean Dieudonné
Author	Dieudonné, Jean Alexandre , 1906-1992
Other name(s)	SpringerLink (Online service)
Publication	Boston : Birkhäuser , 2009.
Physical Details	XXIV, 648 pages : online resource.
Series	Modern Birkhäuser classics
ISBN	9780817649074
Summary Note	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. 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! âMathSciNet [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.â¦ The details are interwoven with the narrative in a very pleasant fashion.â¦ [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:
Contents note	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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-0-8176-4907-4
Links to Related Works	Subject References: Algebraic Topology . Differential Geometry . Global differential geometry . History of mathematics . Mathematica (Computer file) . Mathematics . Authors: Dieudonné, Jean Alexandre 1906-1992 . Corporate Authors: SpringerLink (Online service) . Series: Modern Birkhäuser classics . Classification: 510.9 . 510.9 (DDC 23) .

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A History of Algebraic and Differential Topology, 1900 - 1960

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