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Diffeomorphisms of elliptic 3-manifolds

Autore: Sungbok Hong; et al
Editore: Berlin : Springer, ©2012.
Serie: Lecture notes in mathematics (Springer-Verlag), 2055.
Edizione/Formato:   eBook : Document : EnglishVedi tutte le edizioni e i formati
Banca dati:WorldCat
Sommario:
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  Per saperne di più…
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Genere/forma: Electronic books
Tipo materiale: Document, Risorsa internet
Tipo documento: Internet Resource, Computer File
Tutti gli autori / Collaboratori: Sungbok Hong; et al
ISBN: 364231564X 9783642315640
Numero OCLC: 808999840
Descrizione: 1 online resource (x, 155 p.) : ill.
Contenuti: Elliptic Three-Manifolds and the Smale Conjecture --
Diffeomorphisms and Embeddings of Manifolds --
The Method of Cerf and Palais --
Elliptic Three-Manifolds Containing One-Sided Klein Bottles --
Lens Spaces.
Titolo della serie: Lecture notes in mathematics (Springer-Verlag), 2055.
Responsabilità: Sungbok Hong ... [et al.].
Maggiori informazioni:

Abstract:

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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