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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
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