Homotopy Theory
eBook - PDF

Homotopy Theory

The Mathematical Works of J. H. C. Whitehead

  1. 468 pages
  2. English
  3. PDF
  4. Available on iOS & Android
eBook - PDF

Homotopy Theory

The Mathematical Works of J. H. C. Whitehead

About this book

Homotopy Theory contains all the published mathematical work of J. H. C. Whitehead, written between 1947 and 1955. This volume considers the study of simple homotopy types, particularly the realization of problem for homotopy types. It describes Whitehead's version of homotopy theory in terms of CW-complexes. This book is composed of 21 chapters and begins with an overview of a theorem to Borsuk and the homotopy type of ANR. The subsequent chapters deal with four-dimensional polyhedral, the homotopy type of a special kind of polyhedron, and the combinatorial homotopy I and II. These topics are followed by reviews of other homotopy types, such as group extensions with homotopy operators, cohomology systems, secondary boundary operator, algebraic homotopy, and the G-dual of a semi-exact couple. The last chapters examine the connected complex homotopy types and the second non-vanishing homotopy groups. This book will be of great value to mathematicians.

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Information

Publisher
Pergamon
Year
2014
Print ISBN
9780080098715
eBook ISBN
9781483184760
Topic
Mathematics
Subtopic
Mathematics General
Index
Mathematics

Table of contents

  1. Front Cover
  2. Homotopy Theory
  3. Copyright Page
  4. Table of Contents
  5. EDITORIAL PREFACE
  6. ACKNOWLEDGMENT
  7. PUBLICATIONS OF J. H. C. WHITEHEAD
  8. CHAPTER 1. NOTE ON A THEOREM DUE TO BORSUK
  9. CHAPTER 2. ON THE HOMOTOPY TYPE OF ANR'S
  10. CHAPTER 3. ON SIMPLY CONNECTED, 4-DIMENSIONAL POLYHEDRA (ABSTRACT)
  11. CHAPTER 4. ON SIMPLY CONNECTED, 4-DIMENSIONAL POLYHEDRA
  12. CHAPTER 5. THE HOMOTOPY TYPE OF A SPECIAL KIND OF POLYHEDRON
  13. CHAPTER 6. COMBINATORIAL HOMOTOPY
  14. CHAPTER 7. COMBINATORIAL HOMOTOPY
  15. CHAPTER 8. SIMPLE HOMOTOPY TYPES
  16. CHAPTER 9. ON THE REALIZABILITY OF HOMOTOPY GROUPS
  17. CHAPTER 10. ON GROUP EXTENSIONS WITH OPERATORS
  18. CHAPTER 11. ON THE 3-TYPE OF A COMPLEX
  19. CHAPTER 12. NOTE ON COHOMOLOGY SYSTEMS
  20. CHAPTER 13. THE SECONDARY BOUNDARY OPERATOR
  21. CHAPTER 14. ALGEBRAIC HOMOTOPY THEORY
  22. CHAPTER 15. A CERTAIN EXACT SEQUENCE
  23. CHAPTER 16. ON THE THEORY OF OBSTRUCTIONS
  24. CHAPTER 17. THE G-DUAL OF A SEMI-EXACT COUPLE
  25. CHAPTER 18. ON THE (n+2)-TYPE OF AN (n–1)-CONNECTED COMPLEX n>4)
  26. CHAPTER 19. ON THE EXACT COUPLE OF A CW-TRIAD
  27. CHAPTER 20. ON THE SECOND NON-VANISHING HOMOTOPY GROUPS OF PAIRS AND TRIADS
  28. CHAPTER 21. THE FIRST NON-VANISHING GROUP OF AN (n + 1)-AD
  29. REFERENCES
  30. CONTENTS OF VOLUMES I TO IV