English

On the Smale Conjecture for Diff$(S^4)$

Geometric Topology 2024-10-03 v9 Differential Geometry

Abstract

Recently Watanabe disproved the Smale Conjecture for S4S^4, by showing Diff(S4)SO(5)(S^{4})\neq SO(5). He showed this by proving that their higher homotopy groups are different. Here we prove this more directly by showing π0\pi_{0}Diff(S4)0(S^{4})\neq 0, otherwise a certain loose-cork could not possibly be a loose-cork.

Cite

@article{arxiv.2008.07269,
  title  = {On the Smale Conjecture for Diff$(S^4)$},
  author = {Selman Akbulut},
  journal= {arXiv preprint arXiv:2008.07269},
  year   = {2024}
}

Comments

9 pages, 14 figures, expanded version

R2 v1 2026-06-23T17:54:19.731Z