A history of algebraic and differential topology, 1900-1960
著者
書誌事項
A history of algebraic and differential topology, 1900-1960
Birkhäuser, c1989
- : Boston
- : Basel
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注記
Bibliography: p. [612]-632
Includes indexes
内容説明・目次
- 巻冊次
-
: Boston ISBN 9780817633882
内容説明
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
目次
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.
- 巻冊次
-
: Basel ISBN 9783764333881
内容説明
This text traces the history of algebraic topology, beginning with its creation by Henri Poincare in 1900 and describing in detail the important ideas introduced in the theory before 1960.
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