Termination of Cartan's equivalence method

TL;DR

This paper demonstrates that Cartan's equivalence method, when applied to constant type problems, always terminates at involution or complete reduction, using the groupoid approach and Cartan-Kuranishi theorem.

Contribution

It provides a proof that Cartan's method terminates at involution for constant type problems, connecting groupoid theory with classical equivalence methods.

Findings

Cartan's equivalence method terminates at involution for constant type problems.

Application of groupoid approach to Lie pseudo-groups.

Integration of Cartan-Kuranishi theorem into the termination proof.

Abstract

We apply the language of the groupoid approach to Lie pseudo-groups, and the classical Cartan-Kuranishi theorem, to prove that Cartan's equivalence method terminates at involution (or at complete reduction) for constant type problems.