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Diffeomorphisms of elliptic 3-manifolds

Author: Sungbok Hong; et al
Publisher: Berlin : Springer, ©2012.
Series: Lecture notes in mathematics (Springer-Verlag), 2055.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Database:WorldCat
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  Read more...
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Genre/Form: Electronic books
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Sungbok Hong; et al
ISBN: 364231564X 9783642315640
OCLC Number: 808999840
Description: 1 online resource (x, 155 p.) : ill.
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.
Series Title: Lecture notes in mathematics (Springer-Verlag), 2055.
Responsibility: Sungbok Hong ... [et al.].

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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