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1. Algebraic topology [2002]
 Hatcher, Allen.
 New York : Cambridge University Press, 2002.
 Description
 Book — xii, 544 p. : ill. ; 26 cm.
 Summary

 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 deltacomplexes
 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. MayerVietoris 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. Hspaces 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. EilenbergMacLane 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 omegaspectra
 76. Spectra and homology theories
 77. EckmannHilton duality
 78. Stable splittings of spaces
 79. The loopspace of a suspension
 80. Symmetric products and the DoldThom theorem
 81. Steenrod squares and powers Appendix: topology of cell complexes The compactopen topology.
 (source: Nielsen Book Data)
(source: Nielsen Book Data)
In most mathematics departments at major universities one of the three or four basic firstyear graduate courses is in the subject of algebraic topology. This introductory textbook in algebraic topology is suitable for use in a course or for selfstudy, 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, Hspaces and Hopf algebras, the Brown representability theorem, the James reduced product, the DoldThom theorem, and a full exposition of Steenrod squares and powers. Researchers will also welcome this aspect of the book.
(source: Nielsen Book Data)
 Online
Science Library (Li and Ma)
Science Library (Li and Ma)  Status 

Stacks  
QA612 .H42 2002  Unknown On reserve at Li and Ma Science Library 2hour loan 
MATH215A01
 Course
 MATH215A01  Algebraic Topology
 Instructor(s)
 Kerckhoff, Steven P