The small growth invariants of Goursat distributions

TL;DR

This paper investigates the small growth invariants of Goursat distributions, relating them to structural invariants and exploring their connection through the monster tower and singularities of curves on surfaces.

Contribution

It introduces a new analysis of small growth invariants of Goursat distributions and connects them to previously studied structural invariants.

Findings

Small growth invariants are related to structural invariants.

Connections established via the monster tower.

Insights into singularities of curves on surfaces.

Abstract

This is the second of a pair of papers devoted to the local invariants of Goursat distributions. The study of these distributions naturally leads to a tower of spaces over an arbitrary surface, called the monster tower, and thence to connections with the topic of singularities of curves on surfaces. In the prior paper we studied those invariants of Goursat distributions akin to those of curves on surfaces, which we call structural invariants. In this paper we study invariants arising from the small growth sequence of a Goursat distribution, and relate them to the the structural invariants.