History of Algebraic and Differential Topology, 1900 - 1960

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 examined each significant paper along this route and describes the steps and strategy of its proofs and its relation to other work. Previously, the history of the many technical developments of 20th-century mathematics had seemed to present insuperable obstacles to scholarship. This book demonstrates in the case of topology how these obstacles can be overcome, with enlightening results... Within its chosen boundaries the coverage of this book is superb. Read it!" (MathSciNet) "[The author] traces the development of algebraic and differential topology from the innovative work by Poincare at the turn of the century to the period around 1960. [He] has given a superb account of the growth of these fields... The details are interwoven with the narrative in a very pleasant fashion... [The author] has previous written histories of functional analysis and of algebraic geometry, but neither book was on such a grand scale as this one. He has made it possible to trace the important steps in the growth of algebraic and differential topology, and to admire the hard work and major advances made by the founders." (Zentralblatt MATH)

• Simplicia1 Techniques and Homology.- The Work of Poincar#x00E9;.- The Build-Up of #x201C;Classical#x201D; Homology.- The Beginnings of Differential Topology.- The Various Homology and Cohomology Theories.- The First Applications of Simplicia1 Methods and of Homology.- The Concept of Degree.- Dimension Theory and Separation Theorems.- Fixed Points.- Local Homological Properties.- Quotient Spaces and Their Homology.- Homolagy of Groups and Homogeneous Spaces.- Applications of Homology to Geometry and Analysis.- Homotopy and its Relution to Homology.- Fundamental Group and Covering Spaces.- Elementary Notions and Early Results in Homotopy Theory.- Fibrations.- Homology of Fibrations.- Sophisticated Relations between Homotopy and Homology.- Cohomology Operations.- Generalized Homology and Cohomology.