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Diffeomorphisms of Elliptic 3-Manifolds - Lecture Notes in Mathematics 2055 (Paperback)
  • Diffeomorphisms of Elliptic 3-Manifolds - Lecture Notes in Mathematics 2055 (Paperback)
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Diffeomorphisms of Elliptic 3-Manifolds - Lecture Notes in Mathematics 2055 (Paperback)

(author), (author), (author), (author)
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Paperback 155 Pages / Published: 28/08/2012
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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

Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
ISBN: 9783642315633
Number of pages: 155
Weight: 266 g
Dimensions: 235 x 155 x 9 mm
Edition: 2012 ed.

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