History of Topology (eBook)

I.M. James (Herausgeber)

eBook Download: PDF

1999 | 1. Auflage
1056 Seiten
Elsevier Science (Verlag)
978-0-08-053407-7 (ISBN)

Infos

Topology, for many years, has been one of the most exciting and influential fields of research in modern mathematics. Although its origins may be traced back several hundred years, it was Poincaré, who gave topology wings in a classic series of articles published around the turn of the century. While the earlier history, sometimes called the prehistory, is also considered, this volume is mainly concerned with the more recent history of topology, from Poincaré, onwards.
As will be seen from the list of contents the articles cover a wide range of topics. Some are more technical than others, but the reader without a great deal of technical knowledge should still find most of the articles accessible. Some are written by professional historians of mathematics, others by historically-minded mathematicians, who tend to have a different viewpoint.

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Topology, for many years, has been one of the most exciting and influential fields of research in modern mathematics. Although its origins may be traced back several hundred years, it was Poincare who "e;gave topology wings"e; in a classic series of articles published around the turn of the century. While the earlier history, sometimes called the prehistory, is also considered, this volume is mainly concerned with the more recent history of topology, from Poincare onwards.As will be seen from the list of contents the articles cover a wide range of topics. Some are more technical than others, but the reader without a great deal of technical knowledge should still find most of the articles accessible. Some are written by professional historians of mathematics, others by historically-minded mathematicians, who tend to have a different viewpoint.

Inhalt

Front Cover 1
History of Topology 4
Copyright Page 5
Contents 8
Preface 6
Acknowledgement of illustrations 7
Chapter 1. The emergence of topological dimension theory 12
Chapter 2. The concept of manifold, 1850-1950 36
Chapter 3. Development of the concept of homotopy 76
Chapter 4. Development of the concept of a complex 114
Chapter 5. Differential forms 122
Chapter 6. The topological work of Henri Poincaré 134
Chapter 7. Weyl and the topology of continuous groups 180
Chapter 8. By their fruits ye shall know them: Some remarks on the interaction of general Topology With Other Areas of Mathematics 210
Chapter 9. Absolute neighborhood retracts and shape theory 252
Chapter 10. Fixed point theory 282
Chapter 11. Geometric aspects in the development of knot theory 312
Chapter 12. Topology and physics - a historical essay 370
Chapter 13. Singularities 428
Chapter 14. One hundred years of manifold topology 446
Chapter 15. 3-dimensional topology up to 1960 460
Chapter 16. A short history of triangulation and related matters 502
Chapter 17. Graph theory 514
Chapter 18. The early development of algebraic topology 542
Chapter 19. From combinatorial topology to algebraic topology 572
Chapter 20. p3(S2), H. Hopf, W.K. Clifford, F. Klein 586
Chapter 21. A history of cohomology theory 590
Chapter 22. Fibre bundles, fibre maps 616
Chapter 23. A history of spectral sequences: Origins to 1953 642
Chapter 24. Stable algebraic topology, 1945-1966 676
Chapter 25. A history of duality in algebraic topology 736
Chapter 26. A short history of H-spaces 758
Chapter 27. A history of rational homotopy theory 768
Chapter 28. History of homological algebra 808
Chapter 29. Topologists at conferences 848
Chapter 30. Topologists in Hitler's Germany 860
Chapter 31. The Japanese school of topology 874
Chapter 32. Some topologists 894
Chapter 33. Johann Benedikt Listing 920
Chapter 34. Poul Heegaard 936
Chapter 35. Luitzen Egbertus Jan Brouwer 958
Chapter 36. Max Dehn 976
Chapter 37. Jakob Nielsen and his contributions to topology 990
Chapter 38. Heinz Hopf 1002
Chapter 39. Hans Freudenthal 1020
Chapter 40. Herbert Seifert (1907–1996) 1032
Appendix. Some dates 1040
Index 1044

Produkt-Details

• Erscheint lt. Verlag: 1.8.2006
• Sprache: englisch
• Themenwelt: Sachbuch/Ratgeber
• Themenwelt: Mathematik / Informatik ► Mathematik ► Algebra
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geschichte der Mathematik
• Themenwelt: Naturwissenschaften
• Themenwelt: Technik
• ISBN-10: 0-08-053407-4 / 0080534074
• ISBN-13: 978-0-08-053407-7 / 9780080534077