The Smale Conjecture for lens spaces

2004/10/31 by Sungbok Hong, Hong, Sungbok, Darryl McCullough +3
Mathematics · #57M99 #FOS: Mathematics #Geometric Topology (math.GT) #math.GT #msc:57M99

paper · pdf · doi:10.48550/arxiv.math/0411016

arxiv created 2004/10/31 · arxiv updated 2009/12/01

Abstract

The original Smale Conjecture asserted that the inclusion of the group O(4) of isometries of the round 3-sphere S into the full diffeomorphism group Diff(S) is a homotopy equivalence. The (Generalized) Smale Conjecture asserts that the inclusion of Isom(M) into Diff(M) is a homotopy equivalence whenever M is an elliptic 3-manifold, that is, a closed Riemannian 3-manifold of constant positive curvature. We prove the Smale Conjecture for all lens spaces L(m,q), where m is at least 3.

Related

• Diffeomorphisms of Elliptic 3-Manifolds
• The Generalized Smale Conjecture for 3-manifolds with genus 2 one-sided Heegaard splittings
• The Smale conjecture for Seifert fibered spaces with hyperbolic base orbifold
• Ricci flow and diffeomorphism groups of 3-manifolds
• Lens spaces given from L-space homology 3-spheres