Format:
Online-Ressource (X, 155 p. 22 illus, digital)
ISBN:
9783642315640
Series Statement:
Lecture Notes in Mathematics 2055
Content:
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
Content:
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
Note:
Includes bibliographical references (p. 145-147) and index
Additional Edition:
ISBN 9783642315633
Additional Edition:
Buchausg. u.d.T. Diffeomorphisms of elliptic 3-manifolds Berlin : Springer, 2012 ISBN 9783642315633
Additional Edition:
ISBN 3642315631
Language:
English
Subjects:
Mathematics
Keywords:
Mannigfaltigkeit
;
Dimension 3
;
Riemannsche Metrik
;
Diffeomorphismus
;
Mannigfaltigkeit
;
Dimension 3
;
Riemannsche Metrik
;
Diffeomorphismus
;
Aufsatzsammlung
DOI:
10.1007/978-3-642-31564-0
URL:
Volltext
(lizenzpflichtig)
Author information:
Rubinstein, Hyam 1948-
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