The Smale Conjecture for lens spaces
几何拓扑
2007-05-23 v1
摘要
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.
引用
@article{arxiv.math/0411016,
title = {The Smale Conjecture for lens spaces},
author = {Sungbok Hong and Darryl McCullough and J. Hyam Rubinstein},
journal= {arXiv preprint arXiv:math/0411016},
year = {2007}
}