Differential Geometry of Microlinear Frolicher Spaces IV-1

TL;DR

This paper explores three different approaches to jet bundles within the framework of microlinear Frolicher spaces, providing transformations between these approaches and setting the stage for further detailed analysis.

Contribution

It introduces three distinct methods for studying jet bundles and demonstrates how to convert between these approaches within the context of microlinear Frolicher spaces.

Findings

Three approaches to jet bundles are presented.

Transformations between approaches are established.

Foundations laid for coordinate-based equivalence in future work.

Abstract

The fourth paper of our series of papers entitled "Differential Geometry of Microlinear Frolicher Spaces is concerned with jet bundles. We present three distinct approaches together with transmogrifications of the first into the second and of the second to the third. The affine bundle theorem and the equivalence of the three approaches with coordinates are relegated to a subsequent paper.