Some smooth circle and cyclic group actions on exotic spheres

TL;DR

This paper applies recent advances in stable homotopy theory to construct smooth circle and cyclic group actions on exotic spheres, linking classical transformation group results with modern homotopy insights.

Contribution

It introduces new smooth group actions on exotic spheres using recent progress in stable homotopy groups, extending classical results.

Findings

Constructed smooth circle actions on specific exotic spheres.

Demonstrated cyclic group actions on exotic spheres.

Connected classical transformation group theory with modern homotopy results.

Abstract

Classical work of Lee, Schultz, and Stolz relates the smooth transformation groups of exotic spheres to the stable homotopy groups of spheres. In this note, we apply recent progress on the latter to produce smooth circle and cyclic group actions on certain exotic spheres.