توپولوژی جبری ۲۰۲۰
Algebraic Topology 2020

1. CONTENTS

2. INTRODUCTION

3. § 1. Analytic and Algebraic Topology

4. § 2. Problems and Examples

5. PART I. SIMPLICIAL COMPLEXES

6. Chapter 1. GEOMETRY OF SIMPLICIAL COMPLEXES

7. § 3. Hulls and Stars

8. § 4. Barycentric Stars

9. § 5. Simplicial Mappings

10. § 6. Neighboring Mappings

11. Chapter 2. HOMOLOGY GROUPS AND COHOMOLOGY GROUPS

12. § 7. Orientation. Incidence Numbers

13. § 8. Homology Groups

14. § 9. Examples and Applications

15. § 10. Cohomology Groups

16. § 11. Homotopic Mappings

17. PART II. CHAIN COMPLEXES AND THEIR APPLICATIONS

18. Chapter 3. GENERAL THEORY

19. § 12. Homology Groups of Chain Complexes

20. § 13. Subcomplexes and Factor Complexes

21. § 14. The Boundary Operator

22. Chapter 4. FREE CHAIN COMPLEXES

23. § 15. Modules and Dual Modules

24. § 16. Mappings and Dual Mappings

25. § 17. Free Chain Complexes. Canonical Bases

26. PART III. CELL COMPLEXES. INVARIANCE

27. Chapter 5. CELL COMPLEXES

28. § 18. Cell Decompositions

29. § 19. The Homology Groups of Cell Decompositions

30. § 20. Normal Subdivisions

31. Chapter 6. INVARIANCE OF THE HOMOLOGY GROUPS

32. § 21. Proof of Invariance

33. § 22. Supplements. Generalizations

34. § 23. Results and Applications

35. § 24. Local Homology Groups

36. PART IV. DEVELOPMENT OF THE THEORY

37. Chapter 7. PRODUCTS IN POLYHEDRA

38. § 25. The Cohomology Ring

39. § 26. The Cap Product

40. Chapter 8. MANIFOLDS

41. § 27. Definitions

42. § 28. Complementary Cell Decompositions

43. § 29. The Poincaré Duality Theorem

44. Chapter 9. THE COHOMOLOGY RING OF A MANIFOLD

45. § 30. Products in Manifolds

46. § 31. Product Matrices

47. BIBLIOGRAPHY

48. INDEX