Lifting diffeomorphisms to vector bundles

TL;DR

This paper establishes criteria for when a diffeomorphism of a smooth manifold can be lifted to a linear automorphism of a vector bundle, with examples and special cases explored.

Contribution

It provides new conditions and criteria for lifting diffeomorphisms to vector bundle automorphisms, including metric and complex cases.

Findings

Criteria for lifting diffeomorphisms to vector bundle automorphisms

Examples illustrating the lifting conditions

Extensions to metric and complex vector bundles

Abstract

Criteria for a diffeomorphism of a smooth manifold $M$ to be lifted to a linear automorphism of a given real vector bundle $p\colon V\rightarrow M$, are stated. Examples are included and the metric and complex vector-bundle cases are also considered.