{"product_id":"the-topology-of-fibre-bundles-9780691005485","title":"The Topology of Fibre Bundles","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eFibre bundles are an integral part of differential geometry. This book begins with an introduction to bundles, including such topics as differentiable manifolds and covering spaces. It then provides brief surveys of advanced topics, such as homotopy theory and cohomology theory, before using them to study further properties of fibre bundles.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePart I. THE GENERAL THEORY OF BUNDLES  1. Introduction 3  2. Coordinate bundles and fibre bundles 6  3. Construction of a bundle from coordinate transformations 14  4. The product bundle 16  5. The Ehresmann-Feldbau definition of bundle 18  6. Differentiable manifolds and tensor bundles 20  7. Factor spaces of groups 28  8. The principal bundle and the principal map 35  9. Associated bundles and relative bundles 43  10. The induced bundle 47  11. Homotopies of maps of bundles 49  12. Construction of cross-sections 54  13. Bundles having a totally disconnected group 59  14. Covering spaces 67  Part II. THE HOMOTOPY THEORY OF BUNDLES  15. Homotopy groups 72  16. The operations of Pi1 on Pi n 83  17. The homotopy sequence of a bundle 90  18. The classification of bundles over the n-sphere 96  19. Universal bundles and the classification theorem 100  20. The fibering of spheres by spheres 105  21. The homotopy groups of spheres 110  22. Homotopy groups of the orthogonal groups 114  23. A characteristic map for the bundle Rn+1 over S n 118  24. A characteristic map for the bundle Un over S 2n - 1 124  25. The homotopy groups of miscellaneous manifolds 131  26. Sphere bundles over spheres 134  27. The tangent bundle of S n 140  28. On the non-existence of fiberings of spheres by spheres 144  Part III. THE COHOMOLOGY THEORY OF BUNDLES  29. The stepwise extension of a cross-section 148  30. Bundles of coefficients 151  31. Cohomology groups based on a bundle of coefficients 155  32. The obstruction cocycle 166  33. The difference cochain 169  34. Extension and deformation theorems 174  35. The primary obstruction and the characteristic cohomology class 177  36. The primary difference of two cross-sections 181  37. Extensions of functions, and the homotopy classification of maps 184  38. The Whitney characteristic classes of a sphere bundle 190  39. The Stiefel characteristic classes of differentiable manifolds 199  40. Quadratic forms on manifolds 204  41. Complex analytic manifolds and exterior forms of degree 2 209  Appendix 218  Bibliography 223  Index 228","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":49403669021015,"sku":"9780691005485","price":69.7,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780691005485.jpg?v=1730484205","url":"https:\/\/bookcurl.com\/products\/the-topology-of-fibre-bundles-9780691005485","provider":"Book Curl","version":"1.0","type":"link"}