Colloquium publications.

CONTENTS.

Vii

17. The Betti Numbers.............................. 109
20. The Coefficients of Torsion........................ 111
23. Relation between the Betti Numbers and the Connectivities.................................... 113
25. Congruences and Homologies...................... 114
27. The Fundamental Congruences and Homologies....... 115
31. Bounding k-circuits.............................. 118
35. Invariance of the Coefficients of Torsion............. 120
39. Duality of the Coefficients of Torsion............... 123
CHAPTER V
THE FUNDAMENTAL GROUP AND CERTAIN UNSOLVED PROBLEMS
1. Homotopic and Isotopic Deformations............. 125
3. Isotopy and Order Relations...................... 126
10. The Indicatrix.................................. 129
13. Theorems on Homotopy.......................... 131
15. The Fundamental Group.......................... 132
18. The Group of a Linear Graph..................... 133
22. The Group of a Two-dimensional Complex......... 135
25. The Commutative Group G...................... 138
28. Equivalences and Homologies..................... 140
30. The Poincare Numbers of G...................... 141
36. Covering M anifolds.............................. 145
38. Three-dimensional M anifolds...................... 146
40. The Heegaard Diagram........................... 147
44. The Knot Problem............................... 150