Colloquium publications.

vi

CONTENTS.

28. The Connectivity R1............................. 49
32. Singular Complexes............................. 52
35. Bounding and Non-bounding 1-circuits............. 54
37. Congruences and Homologies, Modulo 2............ 55
39. The Correspondence A........................... 57
47. Invariance of R1........................ 61
50. Invariance of the 2-circuit......................... 62
54. M atrices of Orientation........................... 64
57. Orientable Complexes................... 67
61. Normal Forms for Manifolds...................... 70
CHAPTER III
COMPLEXES AND MANIFOLDS OF N DIMENSIONS
1. Fundamental Definitions.......................... 73
4. M atrices of Incidence............................. 75
9. The Connectivities Ri........................... 77
11. Reduction of the Matrices Hk to Normal Form....... 79
15. Congruences and Homologies, Modulo 2......... 81
17. Theory of the n-Cell.............................. 83
20. Regular Complexes............................... 85
24. M anifolds....................................... 88
25. D ual Com plexes................................. 88
29. Duality of the Connectivities R.................... 91
31. Generalized M anifolds............................ 92
35. Bounding and Non-bounding k-circuits............. 94
42. Invariance of the Connectivities Ri................. 98
CHAPTER IV
ORIENTABLE MANIFOLDS
1. Oriented n-cells................................. 100
5. Matrices of Orientation........................... 103
8. Covering Oriented Complexes.................. 104
10. Boundary of an Oriented Complex............... 105
12. Oriented k-circuits............................... 107
14. Normal Form of Ek............................. 108