Bibliothèque de L'IMIST/CNRST

Includes bibliographical references (pages 612-632) and indexes.

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.

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-