By Sungbok Hong,John Kalliongis,Darryl McCullough,J. Hyam Rubinstein
This paintings issues the diffeomorphism teams of 3-manifolds, specifically of elliptic 3-manifolds. those are the closed 3-manifolds that admit a Riemannian metric of continuing optimistic curvature, referred to now to be precisely the closed 3-manifolds that experience a finite primary workforce. The (Generalized) Smale Conjecture asserts that for any elliptic 3-manifold M, the inclusion from the isometry workforce of M to its diffeomorphism workforce is a homotopy equivalence. the unique Smale Conjecture, for the 3-sphere, used to be confirmed by means of J. Cerf and A. Hatcher, and N. Ivanov proved the generalized conjecture for plenty of of the elliptic 3-manifolds that include a geometrically incompressible Klein bottle.
The major effects determine the Smale Conjecture for all elliptic 3-manifolds containing geometrically incompressible Klein bottles, and for all lens areas L(m,q) with m no less than three. extra effects indicate that for a Haken Seifert-fibered three manifold V, the gap of Seifert fiberings has contractible parts, and except a small record of identified exceptions, is contractible. significant foundational and heritage
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Diffeomorphisms of Elliptic 3-Manifolds (Lecture Notes in Mathematics) by Sungbok Hong,John Kalliongis,Darryl McCullough,J. Hyam Rubinstein