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Diffeomorphisms of elliptic 3-manifolds
This work concerns the diffeomorphism groups of 3-manifolds, in particular of elliptic 3-manifolds. These are the closed 3-manifolds that admit a Riemannian metric of constant positive curvature, now known to be exactly the closed 3-manifolds that have a finite fundamental group. The (Generalized) S...
| Auteurs principaux : | , , , |
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| Autres auteurs : | |
| Format : | Livre |
| Langue : | anglais |
| Titre complet : | Diffeomorphisms of elliptic 3-manifolds / Sungbok Hong, John Kalliongis, Darryl McCullough... [et al.] |
| Édition : | 1st ed. 2012. |
| Publié : |
Berlin, Heidelberg :
Springer Berlin Heidelberg
, [20..] Cham : Springer Nature |
| Collection : | Lecture notes in mathematics (Internet) ; 2055 |
| Accès en ligne : |
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| Condition d'utilisation et de reproduction : | Conditions particulières de réutilisation pour les bénéficiaires des licences nationales : https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 |
| Contenu : | 1 Elliptic 3-manifolds and the Smale Conjecture. 2 Diffeomorphisms and Embeddings of Manifolds. 3 The Method of Cerf and Palais. 4 Elliptic 3-manifolds Containing One-sided Klein Bottles. 5 Lens Spaces |
| Sujets : | |
| Documents associés : | Autre format:
Diffeomorphisms of elliptic 3-manifolds Autre format: Diffeomorphisms of Elliptic 3-Manifolds Autre format: Diffeomorphisms of elliptic 3-manifolds |
| Résumé : | This work concerns the diffeomorphism groups of 3-manifolds, in particular of elliptic 3-manifolds. These are the closed 3-manifolds that admit a Riemannian metric of constant positive curvature, now known to be exactly the closed 3-manifolds that have a finite fundamental group. The (Generalized) Smale Conjecture asserts that for any elliptic 3-manifold M, the inclusion from the isometry group of M to its diffeomorphism group is a homotopy equivalence. The original Smale Conjecture, for the 3-sphere, was proven by J. Cerf and A. Hatcher, and N. Ivanov proved the generalized conjecture for many of the elliptic 3-manifolds that contain a geometrically incompressible Klein bottle.The main results establish the Smale Conjecture for all elliptic 3-manifolds containing geometrically incompressible Klein bottles, and for all lens spaces L(m,q) with m at least 3. Additional results imply that for a Haken Seifert-fibered 3 manifold V, the space of Seifert fiberings has contractible components, and apart from a small list of known exceptions, is contractible. Considerable foundational and background material on diffeomorphism groups is included |
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| Notes : | L'impression du document génère 162 p. Autres contributions : J. Hyam Rubinstein (co-auteur) |
| Bibliographie : | Bibliogr. Index |
| ISBN : | 978-3-642-31564-0 |
| DOI : | 10.1007/978-3-642-31564-0 |