1. Algebraic topology [2002]

Book
xii, 544 p. : ill. ; 26 cm.
  • Part I. Some Underlying Geometric Notions: 1. Homotopy and homotopy type-- 2. Deformation retractions-- 3. Homotopy of maps-- 4. Homotopy equivalent spaces-- 5. Contractible spaces-- 6. Cell complexes definitions and examples-- 7. Subcomplexes-- 8. Some basic constructions-- 9. Two criteria for homotopy equivalence-- 10. The homotopy extension property-- Part II. Fundamental Group and Covering Spaces: 11. The fundamental group, paths and homotopy-- 12. The fundamental group of the circle-- 13. Induced homomorphisms-- 14. Van Kampen's theorem of free products of groups-- 15. The van Kampen theorem-- 16. Applications to cell complexes-- 17. Covering spaces lifting properties-- 18. The classification of covering spaces-- 19. Deck transformations and group actions-- 20. Additional topics: graphs and free groups-- 21. K(G, 1) spaces-- 22. Graphs of groups-- Part III. Homology: 23. Simplicial and singular homology delta-complexes-- 24. Simplicial homology-- 25. Singular homology-- 26. Homotopy invariance-- 27. Exact sequences and excision-- 28. The equivalence of simplicial and singular homology-- 29. Computations and applications degree-- 30. Cellular homology-- 31. Euler characteristic-- 32. Split exact sequences-- 33. Mayer-Vietoris sequences-- 34. Homology with coefficients-- 35. The formal viewpoint axioms for homology-- 36. Categories and functors-- 37. Additional topics homology and fundamental group-- 38. Classical applications-- 39. Simplicial approximation and the Lefschetz fixed point theorem-- Part IV. Cohomology: 40. Cohomology groups: the universal coefficient theorem-- 41. Cohomology of spaces-- 42. Cup product the cohomology ring-- 43. External cup product-- 44. Poincare duality orientations-- 45. Cup product-- 46. Cup product and duality-- 47. Other forms of duality-- 48. Additional topics the universal coefficient theorem for homology-- 49. The Kunneth formula-- 50. H-spaces and Hopf algebras-- 51. The cohomology of SO(n)-- 52. Bockstein homomorphisms-- 53. Limits-- 54. More about ext-- 55. Transfer homomorphisms-- 56. Local coefficients-- Part V. Homotopy Theory: 57. Homotopy groups-- 58. The long exact sequence-- 59. Whitehead's theorem-- 60. The Hurewicz theorem-- 61. Eilenberg-MacLane spaces-- 62. Homotopy properties of CW complexes cellular approximation-- 63. Cellular models-- 64. Excision for homotopy groups-- 65. Stable homotopy groups-- 66. Fibrations the homotopy lifting property-- 67. Fiber bundles-- 68. Path fibrations and loopspaces-- 69. Postnikov towers-- 70. Obstruction theory-- 71. Additional topics: basepoints and homotopy-- 72. The Hopf invariant-- 73. Minimal cell structures-- 74. Cohomology of fiber bundles-- 75. Cohomology theories and omega-spectra-- 76. Spectra and homology theories-- 77. Eckmann-Hilton duality-- 78. Stable splittings of spaces-- 79. The loopspace of a suspension-- 80. Symmetric products and the Dold-Thom theorem-- 81. Steenrod squares and powers-- Appendix: topology of cell complexes-- The compact-open topology.
  • (source: Nielsen Book Data)9780521791601 20160528
In most major universities one of the three or four basic first-year graduate mathematics courses is algebraic topology. This introductory text is suitable for use in a course on the subject or for self-study, featuring broad coverage and a readable exposition, with many examples and exercises. The four main chapters present the basics: fundamental group and covering spaces, homology and cohomology, higher homotopy groups, and homotopy theory generally. The author emphasizes the geometric aspects of the subject, which helps students gain intuition. A unique feature is the inclusion of many optional topics not usually part of a first course due to time constraints: Bockstein and transfer homomorphisms, direct and inverse limits, H-spaces and Hopf algebras, the Brown representability theorem, the James reduced product, the Dold-Thom theorem, and Steenrod squares and powers.
(source: Nielsen Book Data)9780521791601 20160528
In most mathematics departments at major universities one of the three or four basic first-year graduate courses is in the subject of algebraic topology. This introductory textbook in algebraic topology is suitable for use in a course or for self-study, featuring broad coverage of the subject and a readable exposition, with many examples and exercises. The four main chapters present the basic material of the subject: fundamental group and covering spaces, homology and cohomology, higher homotopy groups, and homotopy theory generally. The author emphasizes the geometric aspects of the subject, which helps students gain intuition. A unique feature of the book is the inclusion of many optional topics which are not usually part of a first course due to time constraints, and for which elementary expositions are sometimes hard to find. Among these are: Bockstein and transfer homomorphisms, direct and inverse limits, H-spaces and Hopf algebras, the Brown representability theorem, the James reduced product, the Dold-Thom theorem, and a full exposition of Steenrod squares and powers. Researchers will also welcome this aspect of the book.
(source: Nielsen Book Data)9780521795401 20160528
Science Library (Li and Ma)
MATH-282B-01