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Topological library . Part 2 Characteristic classes and smooth structures on manifolds [[electronic resource] /] / editors, S.P. Novikov, I.A. Taimanov ; translated by V.O. Manturov
| Topological library . Part 2 Characteristic classes and smooth structures on manifolds [[electronic resource] /] / editors, S.P. Novikov, I.A. Taimanov ; translated by V.O. Manturov |
| Pubbl/distr/stampa | Hackensack, N.J., : World Scientific, c2010 |
| Descrizione fisica | 1 online resource (278 p.) |
| Disciplina | 514/.72 |
| Altri autori (Persone) |
NovikovS. P (Sergeĭ Petrovich)
TaĭmanovI. A <1961-> (Iskander Asanovich) |
| Collana | Series on knots and everything |
| Soggetto topico |
Cobordism theory
Characteristic classes Differential topology |
| ISBN |
1-282-76067-X
9786612760679 981-283-687-X |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Contents; S. P. Novikov's Preface; 1 J. Milnor. On manifolds homeomorphic to the 7-sphere; 1. The invariant λ(M7); 2. A partial characterization of the n-sphere; 3. Examples of 7-manifolds; 4. Miscellaneous results; References; 2 M. Kervaire and J. Milnor. Groups of homotopy spheres. I; 1. Introduction; 2. Construction of the group Θn; 3. Homotopy spheres are s-parallelizable; 4. Which homotopy spheres bound parallelizable manifolds?; 5. Spherical modifications; 6. Framed sphericalmodifications; 7. The groups bP2k; 8. A cohomology operation; References
3 S. P. Novikov. Homotopically equivalent smooth manifoldsIntroduction; Chapter I. The fundamental construction; 1. Morse's surgery; 2. Relative π-manifolds; 3. The general construction; 4. Realization of classes; 5. The manifolds in one class; 6. Onemanifold in different classes; Chapter II. Processing the results; 7. The Thom space of a normal bundle. Its homotopy structure; 8. Obstructions to a di.eomorphism of manifolds having the same homotopy type and a stable normal bundle; 9. Variation of a smooth structure keeping triangulation preserved 10. Varying smooth structure and keeping the triangulation preserved.Morse surgeryChapter III. Corollaries and applications; 11. Smooth structures on Cartesian product of spheres; 12. Low-dimensional manifolds. Cases n = 4, 5, 6, 7; 13. Connected sum of a manifold with Milnor's sphere; 14. Normal bundles of smooth manifolds; Appendix 1. Homotopy type and Pontrjagin classes; Appendix 2. Combinatorial equivalence and Milnor's microbundle theory; Appendix 3. On groups ; Appendix 4. Embedding of homotopy spheres into Euclidean space and the suspension stable homomorphism Introduction 1. Formulation of results; 2. The proof scheme of main theorems; 3. A geometrical lemma; 4. An analog of the Hurewicz theorem; 5. The functor P = Homc and its application to the study of homology properties of degree one maps; 6. Stably freeness of kernel modules under the assumptions of Theorem 3; 7. The homology effect of a Morse surgery; 8. Proof of Theorem 3; 9. Proof of Theorem 6; 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 |
| Record Nr. | UNINA-9910811314003321 |
| Hackensack, N.J., : World Scientific, c2010 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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