A Monster Tower Approach to Goursat Multi-Flags

TL;DR

This paper classifies the orbits of a diffeomorphism group action on a tower of fibrations with P2 fibers, advancing the understanding of Goursat 2-flags and providing a detailed orbit classification up to the fourth level.

Contribution

It introduces a new tower approach to classify Goursat multi-flags and provides the first orbit classification for the first four levels of the Monster Tower.

Findings

34 orbits at the fourth level identified

First steps towards classifying Goursat 2-flags of small length

Orbit classification within the first four levels achieved

Abstract

We consider here the problem of classifying orbits of an action of the dif- feomorphism group of 3-space on a tower of fibrations with P2-fibers that generalize the Monster Tower due to Montgomery and Zhitomirskii. As a corollary we give the first steps towards the problem of classifying Goursat 2-flags of small length. In short, we classify the orbits within the first four levels of the Monster Tower and show that there is a total of 34 orbits at the fourth level in the tower.