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Invariants for effective homotopy classification and extension of mappings

About this Title

Paul Olum

Publication: Memoirs of the American Mathematical Society
Publication Year: 1961; Number 37
ISBNs: 978-0-8218-1237-2 (print); 978-0-8218-9980-9 (online)
DOI: https://doi.org/10.1090/memo/0037
MathSciNet review: 0126850

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Table of Contents

Chapters

  • Part I. Introduction and preliminaries
  • 1. Introduction
  • 2. Eilenberg-MacLane groups and cohomology operations
  • 3. Cohomology operations for the case of the second obstruction
  • 4. Binary cohomology operations
  • Part II. Invariants for the extension problem
  • 5. The first level of invariants
  • 6. The second level of invariants
  • 7. The main extension theorems
  • 8. A special case and the retraction theorem
  • Part III. Invariants for the homotopy problem
  • 9. The first level: Difference homomorphisms
  • 10. The second level and the homotopy theorems
  • Part IV. Properties of the extension invariant
  • 11. General properties
  • 12. Comparison formula
  • 13. Coset structure and formula
  • Part V. Properties of the homotopy invariant
  • 14. General properties
  • 15. Addition formula and its consequences; formula for $\Lambda _ {f, f}$
  • 16. An application
  • 17. Appendix 1: More general definition of the invariants
  • 18. Appendix 2: Some homological information
  • 19. Appendix 3: Mapping cylinders