Equivariant homotopy and deformations of diffeomorphisms

TL;DR

This paper develops methods for constructing and deforming diffeomorphisms on manifolds with Lie group actions, advancing understanding of exotic sphere diffeomorphisms and equivariant homotopy of Lie groups.

Contribution

It introduces new techniques for deforming diffeomorphisms respecting Lie group symmetries, with applications to exotic spheres and equivariant homotopy theory.

Findings

Constructed new classes of equivariant diffeomorphisms

Analyzed deformations leading to exotic sphere structures

Enhanced understanding of equivariant homotopy of Lie groups

Abstract

We present a way of constructing and deforming diffeomorphisms of manifolds endowed with a Lie group action. This is applied to the study of exotic diffeomorphisms and involutions of spheres and to the equivariant homotopy of Lie groups.