A History of Algebraic and Differential Topology, 1900 - 1960

• Main Author: Dieudonn,̌ Jean. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: Boston : Birkhũser Boston, 2009.
• Series: Modern Birkhũser Classics
• Subjects: Mathematics.; Global differential geometry.; Mathematics_$xHistory.; Algebraic topology.; Algebraic Topology.; Differential Geometry.; History of Mathematics.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-0-8176-4907-4

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 topolo...

Table of Contents:

• Preface
• Notations
• Part 1. Simplicial Techniques and Homology
• Introduction
• The Work of Poincar ̌
• 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.