Some Relations Between Homology and Homotopy Groups

CONTENTS INTRODUCTION. CHAPTER I. MAIN CONCEPTS AND RESULTS. PAGE 1. Set systems 429 2. Group systems 430 3. The complex S(s) 430 4. The complex K(W) 432 5. The chain transformation K 433 6. The main isomorphism theorem 433 7. Special set systems 433 S. The main theorem for pairs 435 CHAPTER II. PROOFS OF THE GENERAL RESULTS. 9. Homotopy groups and sequences 438 10. Proof of Lemma 1 439 11. Extension theorems 440 12. Additivity theorems 441 13. Singular prisms 442 14. Proof of Lemma 2 443 15. Proof of Theorem I 445 CHAPTER III. PROOFS OF THE SPECIAL RESULTS. 16. Proof of Lemma 3 447 17. Proof of Theorem II (ii) 448 CHAPTER IV. MISCELLANEOUS RESULTS. 18. Cohomology 452 19. Products 456 20. Homomorphisms of group systems 457 21. Mappings of set systems 458 22. More special results 459 23. Computation of integral homology groups . 460