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About This Book
Algebraic and Classical Topology contains all the published mathematical work of J. H. C. Whitehead, written between 1952 and 1960. This volume is composed of 21 chapters, which represent two groups of papers. The first group, written between 1952 and 1957, is principally concerned with fiber spaces and the Spanier-Whitehead S-theory. In the second group, written between 1957 and 1960, Whitehead returns to classical topology after a long interval, and participates in the renewed assault on the problems which fascinated him most. This book will prove useful to mathematicians.
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Table of contents
- Front Cover
- Algebraic and Classical Topology
- Copyright Page
- Table of Contents
- EDITORIAL PREFACE
- ACKNOWLEDGMENT
- PUBLICATIONS OF J. H. C. WHITEHEAD
- CHAPTER 1. ON CERTAIN THEOREMS OF G. W. WHITEHEAD
- CHAPTER 2. NOTE ON THE WHITEHEAD PRODUCT
- CHAPTER 3. NOTE ON FIBRE SPACES
- CHAPTER 4. THE HOMOTOPY THEORY OF SPHERE BUNDLES OVER SPHERES (I)
- CHAPTER 5. THE HOMOTOPY THEORY OF SPHERE BUNDLES OVER SPHERES (II)
- CHAPTER 6. ON FIBRE SPACES IN WHICH THE FIBRE IS CONTRACT!BLE
- CHAPTER 7. OBSTRUCTIONS TO COMPRESSION
- CHAPTER 8. A FIRST APPROXIMATION TO HOMOTOPY THEORY
- CHAPTER 9. THE THEORY OF CARRIERS AND S-THEORY
- CHAPTER 10. DUALITY IN HOMOTOPY THEORY
- CHAPTER 11. DUALITY IN TOPOLOGY
- CHAPTER 12. DUALITY BETWEEN CW-LATTICES
- CHAPTER 13. DUALITY IN RELATIVE HOMOTOPY THEORY
- CHAPTER 14. HOMOLOGY WITH ZERO COEFFICIENTS
- CHAPTER 15. NOTE ON THE CONDITION n-colc
- CHAPTER 16. ON INVOLUTIONS OF SPHERES
- CHAPTER 17. ON 2-SPHERES IN 3-MANIFOLDS
- CHAPTER 18. ON FINITE COCYCLES AND THE SPHERE THEOREM
- CHAPTER 19. A PROOF AND EXTENSION OF DEHN'S LEMMA
- CHAPTER 20. THE IMMERSION OF AN OPEN 3-MANIFOLD IN EUCLIDEAN 3-SPACE
- CHAPTER 21. MANIFOLDS WITH TRANSVERSE FIELDS IN EUCLIDEAN SPACE
- CHAPTER 22. IMBEDDING OF MANIFOLDS IN EUCLIDEAN SPACE
- CONTENTS OF VOLUMES I TO IV