Differential ManifoldsAcademic Press, 1992 M12 3 - 248 páginas Differential Manifolds is a modern graduate-level introduction to the important field of differential topology. The concepts of differential topology lie at the heart of many mathematical disciplines such as differential geometry and the theory of lie groups. The book introduces both the h-cobordism theorem and the classification of differential structures on spheres. The presentation of a number of topics in a clear and simple fashion make this book an outstanding choice for a graduate course in differential topology as well as for individual study.
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Contenido
| 1 | |
Chapter II Immersions Imbeddings Submanifolds | 25 |
Chapter III Normal Bundle Tubular Neighborhoods | 41 |
Chapter IV Transversality | 59 |
Chapter V Foliations | 75 |
Chapter VI Operations on Manifolds | 89 |
Chapter VII Handle Presentation Theorem | 125 |
Chapter VIII The hCobordism Theorem | 143 |
Chapter IX Framed Manifolds | 167 |
Chapter X Surgery | 195 |
Appendix | 223 |
| 233 | |
| 241 | |
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1-handles 1)-connected assume atlas attaching sphere belt sphere chart closed manifold cobordism compact connected manifold connected sum consider construction coordinates Corollary critical points d-field defined definition denoted diagonal diffeomorphism dimension disc bundle disjoint elements equivalent Exercise Show fiber foliation follows framed cobordism framed submanifold given h-cobordism theorem handlebody hence homeomorphic homology class homotopy groups homotopy sphere identity map imbedding implies intersection numbers inverse isomorphism isotopy Jacobian k)-handlebody Lemma Let f Let h map f matrix Morse function n-dimensional neat submanifold normal bundle obtain open subset operation oriented manifold parallelizable Poincaré Poincaré conjecture Pontriagin projection Proof Let Proposition prove regular value simply connected smooth function smooth manifold smooth map smooth structures stably trivial subbundle submanifold submersion Suppose surgery surjective tangent bundle Theorem Let topological tr-manifold transversal trivial normal bundle tubular neighborhood vector field yields