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A history of algebraic and differential topology, 1900-1960

Author: Jean Dieudonné
Publisher: Boston : Birkhäuser, ©1989.
Edition/Format:   Print book : EnglishView all editions and formats
Database:WorldCat
Summary:

Written by a world-renowned mathematician, this well informed and classic text traces the history of algebraic topology, beginning with its creation in the early 1900s. It goes on to describe in  Read more...

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Genre/Form: History
Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Jean Dieudonné
ISBN: 081763388X 9780817633882 376433388X 9783764333881
OCLC Number: 17875894
Notes: Includes indexes.
Description: xxi, 648 pages : illustrations ; 24 cm
Contents: Part 1: Simplicial techniques and homology --
I. The work of Poincaré --
II. The build-up of "classical" homology --
III. The beginnings of differential topology --
IV. The various homology and cohomology theories --
Part 2: The first applications of simplicial methods and of homology --
I. The concept of degree --
II. Dimension theory and separation theorems --
III. Fixed points --
IV. Local homological properties --
V. Quotient spaces and their homology --
VI. Homology of groups and homogeneous spaces --
VII. Applications of homology to geometry and analysis --
Part 3: Homotopy and its relation to homology --
I. Fundamental group and covering spaces --
II. Elementary notions and early results in homotopy theory --
IV. Homology of fibrations --
V. Sophisticated relations between homotopy and homology --
VI. Cohomology operations --
VII. Generalized homology and cohomology.
Responsibility: Jean Dieudonné.
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From the reviews: "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 Read more...

 
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