Chirality in incidence geometry

TL;DR

This paper extends the concept of chirality from abstract polytope theory to general incidence geometries, characterizing automorphism groups of regular and chiral geometries in a Coxeter-like manner.

Contribution

It introduces a broader framework for chiral incidence geometries and provides new characterizations of their automorphism groups, enhancing understanding of their symmetry properties.

Findings

Characterization of automorphism groups of regular geometries

Extension of chirality concepts to incidence geometries

Detailed analysis of the regular case

Abstract

Guided by the ideas of chirality in the abstract polytope theory, the present paper aims to extend the concept to a more general setting of incidence geometries. The purpose of this paper is to explore the more general framework of thin residually connected chiral geometries and also to take this opportunity to look at the regular case in a more detailed way. We give characterisations of automorphism groups of regular and chiral thin residually connected geometries in the same spirit as Coxeter groups.