Diffeomorphisms of Elliptic 3-manifolds - Lecture Notes in Mathematics - Sungbok Hong - Books - Springer-Verlag Berlin and Heidelberg Gm - 9783642315633 - August 28, 2012
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Sungbok Hong
Diffeomorphisms of Elliptic 3-manifolds - Lecture Notes in Mathematics 1st edition

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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

165 pages, 22 black & white illustrations, 3 black & white tables, biography

Media Books     Paperback Book   (Book with soft cover and glued back)
Released August 28, 2012
ISBN13 9783642315633
Publishers Springer-Verlag Berlin and Heidelberg Gm
Pages 165
Dimensions 156 × 234 × 9 mm   ·   244 g
Language English  

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