On The Equivalence Problem for Geometric Structures, II

TL;DR

This paper advances the theory of geometric structure equivalence by establishing criteria for local and global equivalence, with examples including Cartan's Flag Systems and considerations of intransitive structures.

Contribution

It extends the general setup from Part I to provide criteria for equivalence of transitive geometric structures and discusses examples like Cartan's Flag Systems.

Findings

Criteria for local and global equivalence of transitive structures

Application to Cartan's Flag Systems as key example

Initial discussion on intransitive structures with regular orbits

Abstract

This paper is a continuation of Part I where the general setup was developed. Here we discuss the general equivalence problem for geometric structures and provide criteria for the equivalence, local and global, of transitive structures. Cartan's Flag Systems illustrate the theory as a major example and, finally, some attention though little is given to non-transitive structures with regular orbits i.e., intransitivity classes.