Allen Hatcher
Algebraic Topology
Description
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.
Chapter Contents
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 Kampenfs 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. Whiteheadfs 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.
ISBN: 0-521-79160-X
Binding: Hardback
ISBN: 0-521-79540-0
Binding: Paperback
Pages: 500
available from December 2001
Edited by Ellis Cumberbatch, Alistair Fitt
Mathematical Modeling
Case Studies from Industry
Description
Industrial mathematics is growing enormously in popularity around the world. This book deals with real industrial problems from real industries. Presented as a series of case studies by some of the worldfs most active and successful industrial mathematicians, this volume shows clearly how the process of mathematical collaboration with industry can not only work successfully for the industrial partner, but also lead to interesting and important mathematics. The book begins with a brief introduction, where the equations that most of the studies are based upon are summarised. Thirteen different problems are then considered, ranging from cooking of cereal to the analysis of epidemic waves in animal populations. Throughout the work the emphasis is on telling industry what they really want to know. This book is suitable for all final year undergraduates, masterfs students, and Ph.D. students who are working on practical mathematical modeling.
Chapter Contents
Introduction; 1. Fluid mechanical modeling of the scroll compressor Peter D. Howell; 2. Determining the viscosity of a carbon paste used in smelting Alistair Fitt; 3. The vibrating element densitometer Ellis Cumberbatch; 4. Acoustic emission from FRP damages hoop-wrapped cylinders D. Rex Westbrook; 5. Modeling the cooking of a single cereal grain Kerry A. Landman and Mark J. McGuinness; 6. Epidemic waves in animal populations: a case study Britta Basse and Graeme C. Wake; 7. Dynamics of automotive catalytic converters Donald Schwendeman; 8. Analysis of an endothermic reaction in a packed column Andrew C. Fowler; 9. Simulation of the temperature behavior of hot glass during cooling Helmut Neunzert, Norbert Siedow and Frank Zingsheim; 10. Water equilibration in vapor-diffusion crystal growth Arnon Chait, Elizabeth Gray and Gerald W. Young; 11. Modeling of quasi-static and dynamic load responses of filled viscoelastic materials H. T. Banks, Gabriella A. Pinter, Laura K. Potter, Michael J. Gaitens and Lynn C. Yanyo; 12. A gasdynamic-acoustic model of a bird scare gun Sjoerd W. Rienstra; 13. Paper tension variations in a printing press Colin P. Please.
ISBN: 0-521-65007-0
Binding: Hardback
ISBN: 0-521-01173-6
Binding: Paperback
Size: 236 x 159 mm
Pages: 316
Weight: 0.562kg
Figures: 93 line diagrams
Published: 18 October 2001