Chirality in incidence geometry

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.