Diffeomorphisms of elliptic 3-manifolds
- Sungbok Hong ... [et al.].
- Heidelberg ; New York : Springer Verlag, c2012.
- Physical description
- x, 155 p. : ill. ; 23 cm.
- Lecture notes in mathematics (Springer-Verlag) 2055.
Math & Statistics Library
QA3 .L28 V.2055
- Unknown QA3 .L28 V.2055
- Includes bibliographical references (p. 145-147) and index.
- 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.
- (source: Nielsen Book Data)
- Publisher's 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.
(source: Nielsen Book Data)
- Publication date
- Lecture notes in mathematics ; 2055
- Additional authors: John Kalliongis, Darryl McCullough, J. Hyam Rubinstein.