Diffeomorphisms of Elliptic 3-Manifolds
Springer Berlin (Verlag)
978-3-642-31563-3 (ISBN)
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
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
| Erscheint lt. Verlag | 28.8.2012 |
|---|---|
| Reihe/Serie | Lecture Notes in Mathematics |
| Zusatzinfo | X, 155 p. 22 illus. |
| Verlagsort | Berlin |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Gewicht | 268 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Geometrie / Topologie |
| Schlagworte | 3-manifold • 57M99, 57S10, 58D05, 58D29 • Elliptic • Frechet • Smale Conjecture |
| ISBN-10 | 3-642-31563-1 / 3642315631 |
| ISBN-13 | 978-3-642-31563-3 / 9783642315633 |
| Zustand | Neuware |
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