Diffeomorphisms of elliptic 3-manifolds /

Diffeomorphisms of elliptic 3-manifolds /

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Bibliographic Details
Imprint:	Berlin : Springer, ©2012.
Description:	1 online resource (x, 155 pages) : illustrations.
Language:	English
Series:	Lecture notes in mathematics, 1617-9692 ; 2055 Lecture notes in mathematics (Springer-Verlag) ; 2055.
Subject:	Diffeomorphisms. Three-manifolds (Topology) Diffeomorphisms. Three-manifolds (Topology)
Format:	E-Resource Book
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/11077237

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Other authors / contributors:	Hong, Sungbok.
ISBN:	364231564X 9783642315640 3642315631 9783642315633
Notes:	Includes bibliographical references and index. Online resource; title from PDF title page (SpringerLink, viewed Sep. 3, 2012).
Summary:	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.

Table of Contents:

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.