Diffeomorphisms of Elliptic 3-Manifolds
Hong, Sungbok.
Diffeomorphisms of Elliptic 3-Manifolds [electronic resource] / by Sungbok Hong, John Kalliongis, Darryl McCullough, J. Hyam Rubinstein. - X, 155 p. 22 illus. online resource. - Lecture Notes in Mathematics, 2055 0075-8434 ; . - Lecture Notes in Mathematics, 2055 .
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.
9783642315640
10.1007/978-3-642-31564-0 doi
Cell aggregation--Mathematics.
Manifolds and Cell Complexes (incl. Diff.Topology).
QA613-613.8 QA613.6-613.66
514.34
Diffeomorphisms of Elliptic 3-Manifolds [electronic resource] / by Sungbok Hong, John Kalliongis, Darryl McCullough, J. Hyam Rubinstein. - X, 155 p. 22 illus. online resource. - Lecture Notes in Mathematics, 2055 0075-8434 ; . - Lecture Notes in Mathematics, 2055 .
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.
9783642315640
10.1007/978-3-642-31564-0 doi
Cell aggregation--Mathematics.
Manifolds and Cell Complexes (incl. Diff.Topology).
QA613-613.8 QA613.6-613.66
514.34