Seifert and Threlfall: A Textbook of Topology

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