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Diffeomorphisms of Elliptic 3-Manifolds

Hong, Sungbok. ; Kalliongis, John. ; McCullough, Darryl. ; Rubinstein, J. Hyam.
Imprint: Berlin, Heidelberg : Springer Berlin Heidelberg : 2012.-
Pages: X, 155 p. 22 illus.

ISBN: 9783642315640
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.

Seria Title: Lecture Notes in Mathematics,


Subject Category: Mathematics. Cell aggregation
Web-Page: http://dx.doi.org/10.1007/978-3-642-31564-0
 Record created 2013-07-22, last modified 2014-02-22


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