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Algebraic Topology
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Numero oggetto eBay:177410348892
Specifiche dell'oggetto
- Condizione
- Book Title
- Algebraic Topology
- EAN
- 8581000033264
- ISBN
- 0521795400
Informazioni su questo prodotto
Product Identifiers
Publisher
Cambridge University Press
ISBN-10
0521795400
ISBN-13
9780521795401
eBay Product ID (ePID)
1728292
Product Key Features
Number of Pages
556 Pages
Language
English
Publication Name
Algebraic Topology
Subject
Topology
Publication Year
2001
Type
Textbook
Subject Area
Mathematics
Format
Perfect
Dimensions
Item Height
1.3 in
Item Weight
34.1 Oz
Item Length
10 in
Item Width
7 in
Additional Product Features
Intended Audience
Scholarly & Professional
LCCN
00-065166
Reviews
'... clear and concise ... makes the book useful both as a basis for courses and as a reference work.' Monatshefte für Mathematik, ' … this is a marvellous tome, which is indeed a delight to read. This book is destined to become very popular amongst students and teachers alike.' Bulletin of the Belgian Mathematical Society, '… clear and concise … makes the book useful both as a basis for courses and as a reference work.' Monatshefte fr Mathematik, '… the truly unusual abundance of instructive examples and complementing exercises is absolutely unique of such a kind … the distinctly circumspect, methodologically inductive, intuitive, descriptively elucidating and very detailed style of writing give evidence to the fact that the author's first priorities are exactly what students need when working with such a textbook, namely clarity, readability, steady motivation, guided inspiration, increasing demand, and as much self-containedness of the exposition as possible. No doubt, a very devoted and experienced teacher has been at work here, very much so to the benefit of beginners in the field of algebraic topology, instructors, and interested readers in general.' Zentralblatt MATH, ' ... this is a marvellous tome, which is indeed a delight to read. This book is destined to become very popular amongst students and teachers alike.' Bulletin of the Belgian Mathematical Society, "This book is one of the most interesting and accessible texts to come out in recent year...The style is refreshingly informal, although precise definitions are always given...this is a very 'student-friendly' approach (very different from the texts which always look for the greatest generality). There are many excellent examples...this will be a major achievement which will help a great many serious students." Mathematical Reviews, '... the truly unusual abundance of instructive examples and complementing exercises is absolutely unique of such a kind ... the distinctly circumspect, methodologically inductive, intuitive, descriptively elucidating and very detailed style of writing give evidence to the fact that the author's first priorities are exactly what students need when working with such a textbook, namely clarity, readability, steady motivation, guided inspiration, increasing demand, and as much self-containedness of the exposition as possible. No doubt, a very devoted and experienced teacher has been at work here, very much so to the benefit of beginners in the field of algebraic topology, instructors, and interested readers in general.' Zentralblatt MATH, "Algebraic topoligy books that emphasize geometrical intuition usually have only a modest technical reach. Remarkably, Hatcher (Cornell Univ.) offers a highly geometrical treatment that neverheless matches the coverage of, e.g., Edwin Henry Spanier's very formidable and identically titled classic work... He promises two advanced companion volumes, one on spectral sequences, one on vector bundles. One anticipates the combined treatise doing for algebraic topology what Michael Spivak's magisterial five-volume set did for differential geometry." Choice
Dewey Edition
21
Illustrated
Yes
Dewey Decimal
514/.2
Table Of Content
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. Poincaré 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.
Synopsis
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., 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., An introductory textbook 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., This introductory textbook is suitable for use in a first-year graduate course or for self-study, featuring broad coverage of the subject and a readable exposition, with many examples and exercises. Along with the basic material on fundamental group and covering spaces, homology and cohomology, higher homotopy groups, and homotopy theory, the book includes many optional topics for which elementary expositions are hard to find.
LC Classification Number
QA612 .H42 2002
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Adi Swoosh Discounter
98,6% di Feedback positivi•661 oggetti venduti
Registrato come venditore privatoPertanto non si applicano i diritti dei consumatori derivanti dalla normativa europea. La Garanzia cliente eBay è comunque applicabile alla maggior parte degli acquisti. Scopri di piùScopri di più
Feedback sul venditore (187)
- 1***l (355)- Feedback lasciato dall'acquirente.Mese scorsoAcquisto verificatoBook was advertised as in ‘Good’ condition, but is terrible condition after you actually open the book. I reached out to the seller saying that it is unreadable and sent multiple photos of heavy ink underlining on dozens and dozens of pages throughout the book. Ink writing in margins, chapter titles, etc. seller offered a 50% refund and I again responded that the book is unreadable. He stated that was in ‘good’ condition when he sent it, eBay has standards and this book is in poor condition.
- a***l (184)- Feedback lasciato dall'acquirente.Ultimi 6 mesiAcquisto verificatoItem was well packed and shipped quickly. Item received was as described. Would do business again.The Black Cauldron (Disney Gold Classic Collection) [DVD] (N° 177260961666)
- x***u (670)- Feedback lasciato dall'acquirente.Mese scorsoAcquisto verificatoReceived on time even faster. Books as described. Good job