The Smale Conjecture for lens spaces

Hong, Sungbok; McCullough, Darryl; Rubinstein, J. Hyam

The Smale Conjecture for lens spaces

Authors

Hong, Sungbok

McCullough, Darryl

Rubinstein, J. Hyam

Description

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.