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Record Nr. |
UNISA996466475203316 |
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Autore |
Hong Sungbok |
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Titolo |
Diffeomorphisms of Elliptic 3-Manifolds [[electronic resource] /] / by Sungbok Hong, John Kalliongis, Darryl McCullough, J. Hyam Rubinstein |
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Pubbl/distr/stampa |
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Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2012 |
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ISBN |
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Edizione |
[1st ed. 2012.] |
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Descrizione fisica |
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1 online resource (X, 155 p. 22 illus.) |
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Collana |
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Lecture Notes in Mathematics, , 0075-8434 ; ; 2055 |
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Disciplina |
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Soggetti |
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Manifolds (Mathematics) |
Complex manifolds |
Manifolds and Cell Complexes (incl. Diff.Topology) |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Bibliographic Level Mode of Issuance: Monograph |
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Nota di bibliografia |
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Includes bibliographical references (p. 145-147) and index. |
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Nota di contenuto |
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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. |
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Sommario/riassunto |
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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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