UID:
almahu_9947367144902882
Umfang:
1 online resource (461 p.)
ISBN:
1-281-76755-7
,
9786611767556
,
0-08-087405-3
Serie:
Pure and applied mathematics, a series of monographs and textbooks ; 89
Originaltitel:
Lehrbuch der Topologie.
Inhalt:
Seifert and Threlfall, A textbook of topology
Anmerkung:
Translation of Lehrbuch der Topologie, and of an article from Acta mathematica, v. 60, p. 147-288, with the title "Topologie dreidimensionaler gefaserler Raume."
,
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
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11. The Schema of a Simplicial Complex12. 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
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27. Singular Homology Groups28. 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
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40. Surfaces with Boundary41. 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
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54. Base Path and Covering Path55. 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
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71. Dual Bases
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English
Weitere Ausg.:
ISBN 0-12-634850-2
Sprache:
Englisch
