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＜電子ブック＞
Diffeomorphisms of Elliptic 3-Manifolds / by Sungbok Hong, John Kalliongis, Darryl McCullough, J. Hyam Rubinstein
(Lecture Notes in Mathematics. ISSN:16179692 ; 2055)

版	1st ed. 2012.
出版者	Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
出版年	2012
本文言語	英語
大きさ	X, 155 p. 22 illus : online resource
著者標目	*Hong, Sungbok author Kalliongis, John author McCullough, Darryl author Rubinstein, J. Hyam author SpringerLink (Online service)
件　名	LCSH:Manifolds (Mathematics) FREE:Manifolds and Cell Complexes
一般注記	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 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 HTTP:URL=https://doi.org/10.1007/978-3-642-31564-0

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