EAN: 9783642315633

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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

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18.03.2025 um 18:27 Uhr

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