Seifert and Threlfall, A textbook of topology

Front Cover

Seifert and Threlfall: A Textbook of Topology and Seifert: Topology of 3-Dimensional Fibered Spaces

Copyright Page

CONTENTS

Preface to English Edition

Acknowledgments

Preface to German Edition

PART I: SEIFERT AND THRELFALL: A TEXTBOOK OF TOPOLOGY

CHAPTER ONE. ILLUSTRATIVE MATERIAL

1. The Principal Problem of Topology

2. Closed Surfaces

3. Isotopy, Homotopy, Homology

4. Higher Dimensional Manifolds

CHAPTER TWO. SIMPLICIAL COMPLEXES

5. Neighborhood Spaces

6. Mappings

7. Point Sets in Euclidean Spaces

8. Identification Spaces

9. n-Simplexes

10. Simplicial Complexes

11. The Schema of a Simplicial Complex

12. Finite, Pure, Homogeneous Complexes

13. Normal Subdivision

14. Examples of Complexes

CHAPTER THREE. HOMOLOGY GROUPS

15. Chains

16. Boundary, Closed Chains

17. Homologous Chains

18. Homology Groups

19. Computation of the Homology Groups in Simple Cases

20. Homologies with Division

21. Computation of Homology Groups from the Incidence Matrices

22. Block Chains

23. Chains mod 2, Connectivity Numbers, Euler’s Formula

24. Pseudomanifolds and Orientability

CHAPTER FOUR. SIMPLICIAL APPROXIMATIONS

25. Singular Simplexes

26. Singular Chains

27. Singular Homology Groups

28. The Approximation Theorem, Invariance of Simplicial Homology Groups

29. Prisms in Euclidean Spaces

30. Proof of the Approximation Theorem

3I. Deformation and Simplicial Approximation of Mappings

CHAPTER FIVE. LOCAL PROPERTIES

32. Homology Groups of a Complex at a Point

33. Invariance of Dimension

34. Invariance of the Purity of a Complex

35. Invariance of Boundary

36. Invariance of Pseudomanifolds and of Orientability

CHAPTER SIX. SURFACE TOPOLOGY

37. Closed Surfaces

38. Transformation to Normal Form

39. Types of Normal Form: The Principal Theorem

40. Surfaces with Boundary

41. Homology Groups of Surfaces

CHAPTER SEVEN. THE FUNDAMENTAL GROUP

42. The Fundamental Group

43. Examples

44. The Edge Path Group of a Simplicial Complex

45. The Edge Path Group of a Surface Complex

46. Generators and Relations

47. Edge Complexes and Closed Surfaces

48. The Fundamental and Homology Groups

49. Free Deformation of Closed Paths

50. Fundamental Group and Deformation of Mappings

51. The Fundamental Group at a Point

52. The Fundamental Group of a Composite Complex

CHAPTER EIGHT. COVERING COMPLEXES

53. Unbranched Covering Complexes

54. Base Path and Covering Path

55. Coverings and Subgroups of the Fundamental Group

56. Universal Coverings

57. Regular Coverings

58. The Monodromy Group

CHAPTER NINE. 3-DIMENSIONAL MANIFOLDS

59. General Principles

60. Representation by a Polyhedron

61. Homology Groups

62. The Fundamental Group

63. The Heegaard Diagram

64. 3-Dimensional Manifolds with Boundary

65. Construction of 3-Dimensional Manifolds out of Knots

CHAPTER TEN. n-DIMENSIONAL MANIFOLDS

66. Star Complexes

67. Cell Complexes

68. Manifolds

69. The Poincaré Duality Theorem

70. Intersection Numbers of Cell Chains

71. Dual Bases

72. Cellular Approximations

73. Intersection Numbers of Singular Chains

74. lnvariance of Intersection Numbers

75. Examples

76. Orientability and Two-Sidedness

77. Linking Numbers

CHAPTER ELEVEN. CONTINUOUS MAPPINGS

78. The Degree of a Mappings

79. A Trace Formula

80. A Fixed Point Formula

81. Applications

CHAPTER TWELVE. AUXILIARY THEOREMS FROM THE THEORY OF GROUPS

82. Generators and Relations

83. Homomorphic Mappings and Factor Groups

84. Abelianization of Groups

85. Free and Direct Products

86. Abelian Groups

87. The Normal Form of Integer Matrices

COMMENTS

BIBLIOGRAPHY

PART II: SEIFERT: TOPOLOGY OF 3-DIMENSIONAL FIBERED SPACES

1. Fibered Spaces

2. Orbit Surface

3. Fiberings of S3

4. Triangulations of Fibered Spaces

5. Drilling and Filling (Surgery)

6. Classes of Fibered Spaces

7. The Orientable Fibered Spaces

8. The Nonorientable Fibered Spaces

9. Covering Spaces

10. Fundamental Groups of Fibered Spaces

11. Fiberings of the 3-Sphere (Complete List)

12. The Fibered Poincaré Spaces

13. Constructing Poincaré Spaces from Torus Knots

14. Translation Groups of Fibered Spaces

15. Spaces Which Cannot Be Fibered

Appendix. Branched Coverings

Index to "A Textbook of Topology"