The Generalized Stokes theorem for R-linear forms on Lie algebroids

TL;DR

This paper extends the classical Stokes theorem to R-linear forms on Lie algebroids, including non-local forms, and demonstrates its application in relating homotopic Lie algebroid homomorphisms through chain operators.

Contribution

It introduces a generalized Stokes theorem for R-linear forms on Lie algebroids and applies it to establish a link between homotopic homomorphisms via chain operators.

Findings

Generalized Stokes theorem for R-linear forms on Lie algebroids.

Application to homotopic Lie algebroid homomorphisms.

Existence of chain operators connecting pullbacks of homotopic maps.

Abstract

The author presents the generalized Stokes theorem for R-linear forms on Lie algebroids (which can be non-local). We apply the Stokes formula on forms to prove that two homotopic homomorphisms of Lie algebroids implies the existence of a chain operator joining their pullback operators.