Characteristic Classes of Lie Algebroid Morphisms

TL;DR

This paper generalizes the concept of characteristic classes from Lie algebroids to morphisms between them, revealing that the simplest class aligns with the modular class, thus broadening the theoretical framework.

Contribution

It extends Fernandes' secondary characteristic classes to base-preserving morphisms between Lie algebroids, introducing a new class that generalizes existing concepts.

Findings

The simplest characteristic class of the morphism coincides with its modular class.

The construction applies to base-preserving morphisms, broadening the scope of characteristic classes.

Provides a unified framework linking characteristic classes and modular classes.

Abstract

We extend R. Fernandes' construction of secondary characteristic classes of a Lie algebroid to the case of a base-preserving morphism between two Lie algebroids. Like in the case of a Lie algebroid, the simplest characteristic class of our construction coincides with the modular class of the morphism.