The Generalized Smale Conjecture for 3-manifolds with genus 2 one-sided Heegaard splittings

Details The Generalized Smale Conjecture for 3-manifolds with genus 2 one-sided Heegaard splittings The Generalized Smale Conjecture for 3-manifolds with genus 2 one-sided Heegaard splittings

1997-12-07

arxiv.org/abs/math/9712233v1

Mathematics

Geometric Topology

23 pages

Scientific paper

The Generalized Smale Conjecture asserts that if M is a closed 3-manifold with constant positive curvature, then the inclusion of the group of isometries into the group of diffeomorphisms is a homotopy equivalence. For the 3-sphere, this was the classical Smale Conjecture proved by A. Hatcher. N. Ivanov proved the Generalized Smale Conjecture for the M which contain a 1-sided Klein bottle and such that no Seifert fibering is nonsingular on the complement of any vertical Klein bottle. We prove it in all remaining cases containing a one-sided Klein bottle, except for the lens space L(4,1).

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