A History of Algebraic and Differential Topology, 1900 - 1960 (Paperback)

Preface.- Notations.- Part 1. Simplicial Techniques and Homology.- Introduction.- The Work of Poincare.- 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.