Front cover image for A history of algebraic and differential topology, 1900-1960

A history of algebraic and differential topology, 1900-1960

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 Poincare, de Rham, Cartan, Hureqicz, and many others, this historical book also focuses on the emergence of new ideas and methods that have led 21st-
eBook, English, ©2009
Birkhäuser, Boston, Mass., ©2009
History
1 online resource (xxi, 648 pages) : illustrations
9780817649074, 0817649077
432711002
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
Originally published in 1989
English