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Topological Library - Part 2 : Characteristic Classes And Smooth Structures On Manifolds.
This is the second of a three-volume set collecting the original and now-classic works in topology written during the 1950s-1960s. The original methods and constructions from these works are properly documented for the first time in this book. No existing book covers the beautiful ensemble of method...
| Clasificación: | Libro Electrónico |
|---|---|
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
World Scientific
2009.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Cover13;
- Contents
- S.P. Novikovs Preface
- 1 J. Milnor. On manifolds homeomorphic to the 7-sphere
- 167; 1. The invariant 955;(M7)
- 167; 2. A partial characterization of the n-sphere
- 167; 3. Examples of 7-manifolds
- 167; 4. Miscellaneous results
- References
- 2 M. Kervaire and J. Milnor. Groups of homotopy spheres. I
- 167;1. Introduction
- 167; 2. Construction of the group 920;n
- 167; 3. Homotopy spheres are s-parallelizable
- 167; 4. Which homotopy spheres bound parallelizable manifolds?
- 167; 5. Spherical modifications
- 167; 6. Framed sphericalmodifications
- 167; 7. The groups bP2k
- 167; 8. A cohomology operation
- References
- 3 S.P. Novikov. Homotopically equivalent smooth manifolds
- Introduction
- Chapter I. The fundamental construction
- 167; 1. Morses surgery
- 167; 2. Relative 960;-manifolds
- 167; 3. The general construction
- 167; 4. Realization of classes
- 167; 5. The manifolds in one class
- 167; 6. Onemanifold in different classes
- Chapter II. Processing the results
- 167; 7. The Thom space of a normal bundle. Its homotopy structure
- 167; 8. Obstructions to a di.eomorphism of manifolds having the same homotopy type and a stable normal bundle
- 167; 9. Variation of a smooth structure keeping triangulation preserved
- 167; 10. Varying smooth structure and keeping the triangulation preserved. Morse surgery
- Chapter III. Corollaries and applications
- 167; 11. Smooth structures on Cartesian product of spheres
- 167; 12. Low-dimensional manifolds. Cases n = 4, 5, 6, 7
- 167; 13. Connected sum of a manifold with Milnors sphere
- 167; 14. Normal bundles of smooth manifolds
- Appendix 1. Homotopy type and Pontrjagin classes
- Appendix 2. Combinatorial equivalence and Milnors microbundle theory
- Appendix 3. On groups
- Appendix 4. Embedding of homotopy spheres into Euclidean space and the suspension stable homomorphism
- References
- 4 S.P. Novikov. Rational Pontrjagin classes. Homeomorphism and homotopy type of closed manifolds
- Introduction
- 167; 1. Signature of a cycle and its properties
- 167; 2. The basic lemma
- 167; 3. Theorems on homotopy invariance. Generalized signature theorem
- 167; 4. The topological invariance theorem
- 167; 5. Consequences of the topological invariance theorem
- Appendix (V.A. Rokhlin). Diffeomorphisms of the manifold S2 215; S3
- References
- 5 S.P. Novikov. On manifolds with free abelian fundamental group and their applications (Pontrjagin classes, smooth structures, high-dimensional knots)
- Introduction
- 167; 1. Formulation of results
- 167; 2. The proof scheme of main theorems
- 167; 3. A geometrical lemma
- 167; 4. An analog of the Hurewicz theorem
- 167; 5. The functor P = Homc and its application to the study of homology properties of degree one maps
- 167; 6. Stably freeness of kernel modules under the assumptions of Theorem 3
- 167; 7. The homology effect of a Morse surgery
- 167; 8. Proof of Theorem 3
- 167; 9. Proof of Theorem 6
- 167; 10. One generalization of Theorem 5
- Appendix 1. On the signature formula
- Appendix 2. Unsolved questions concerning characteristic class theory
- Appendix 3. Algebraic remarks about the functor P = Homc
- References
- 6 R. Kirby. Stable homeomorphisms and the annulus conjecture.