//]]>
Normal View MARC View ISBD View

Diffeomorphisms of Elliptic 3-Manifolds

by Hong, Sungbok.
Authors: Kalliongis, John.%author. | McCullough, Darryl.%author. | Rubinstein, J. Hyam.%author. | SpringerLink (Online service) Series: Lecture Notes in Mathematics, 0075-8434 ; . 2055 Physical details: X, 155 p. 22 illus. online resource. ISBN: 364231564X Subject(s): Mathematics. | Cell aggregation %Mathematics. | Mathematics. | Manifolds and Cell Complexes (incl. Diff.Topology).
Tags from this library:
No tags from this library for this title.
Item type Location Call Number Status Date Due
E-Book E-Book AUM Main Library 514.34 (Browse Shelf) Not for loan

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.

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.

There are no comments for this item.

Log in to your account to post a comment.