Diffeomorphisms of Elliptic 3-Manifolds / by Sungbok Hong, John Kalliongis, Darryl McCullough, J. Hyam Rubinstein.

Format:

Book

Author/Creator:

Hong, Sungbok, author.

Kalliongis, John, author.

McCullough, Darryl, 1951- author.

Rubinstein, Joachim Hyam, author.

Contributor:

SpringerLink (Online service)

Series:

Lecture Notes in Mathematics, 0075-8434 ; 2055.

Lecture Notes in Mathematics, 0075-8434 ; 2055

Language:

English

Subjects (All):

Cell aggregation--Mathematics.

Cell aggregation.

Manifolds and Cell Complexes (incl. Diff.Topology).

Local Subjects:

Manifolds and Cell Complexes (incl. Diff.Topology).

Physical Description:

1 online resource (X, 155 pages 22 illustrations).

Contained In:

Springer eBooks

Place of Publication:

Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2012.

System Details:

text file PDF

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.

Contents:

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.

Other Format:

Printed edition:

ISBN:

9783642315640

Access Restriction:

Restricted for use by site license.