02526nmm a2200325 u 4500001001200000003002700012005001700039007002400056008004100080020001800121100001800139245014200157250001700299260006300316300004000379505021400419653002200633653005500655653002800710700003100738700003300769700003400802710003400836041001900870989003600889490003300925856007200958082001101030520115901041EB000389807EBX0100000000000000024286000000000000000.0cr|||||||||||||||||||||130626 ||| eng a97836423156401 aHong, Sungbok00aDiffeomorphisms of Elliptic 3-ManifoldshElektronische Ressourcecby Sungbok Hong, John Kalliongis, Darryl McCullough, J. Hyam Rubinstein a1st ed. 2012 aBerlin, HeidelbergbSpringer Berlin Heidelbergc2012, 2012 aX, 155 p. 22 illusbonline resource0 a1 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 aComplex manifolds aManifolds and Cell Complexes (incl. Diff.Topology) aManifolds (Mathematics)1 aKalliongis, Johne[author]1 aMcCullough, Darryle[author]1 aRubinstein, J. Hyame[author]2 aSpringerLink (Online service)07aeng2ISO 639-2 bSpringeraSpringer eBooks 2005-0 aLecture Notes in Mathematics uhttps://doi.org/10.1007/978-3-642-31564-0?nosfx=yxVerlag3Volltext0 a514.34 aThis 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