Pushforward and smooth vector pseudo-bundles

TL;DR

This paper introduces a pushforward operation for diffeological vector pseudo-bundles, enabling new constructions and applications in smooth geometry, and connecting classical vector bundle theory with diffeology.

Contribution

It defines a pushforward operation as left adjoint to pullback, producing new examples and applications in the context of diffeological vector pseudo-bundles.

Findings

Pushforward operation is established for diffeological vector pseudo-bundles.

New concrete examples of projective diffeological vector spaces are constructed.

Applications include smooth splittings related to geometry.

Abstract

In this paper, we study a new operation named pushforward on diffeological vector pseudo-bundles, which is left adjoint to the pullback. We show how to pushforward projective diffeological vector pseudo-bundles to get projective diffeological vector spaces, producing many concrete new examples, together with application to smooth splittings of some projective diffeological vector spaces related to geometry. This brings new objects to diffeology from classical vector bundle theory.