Diffeomorphisms of Elliptic 3-Manifolds / Lecture Notes in Mathematics Bd.2055 (PDF)
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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.
- Autoren: Sungbok Hong , John Kalliongis , Darryl McCullough , J. Hyam Rubinstein
- 2012, 2012, 155 Seiten, Englisch
- Verlag: Springer-Verlag GmbH
- ISBN-10: 364231564X
- ISBN-13: 9783642315640
- Erscheinungsdatum: 29.08.2012
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