On residual connectedness in chiral geometries

TL;DR

This paper proves that chiral coset geometries derived from $C^+$-groups inherently possess residual connectedness, classifying them as hypertopes, which advances understanding of their structural properties.

Contribution

It establishes that all chiral coset geometries from $C^+$-groups are residually connected and are hypertopes, providing a new insight into their geometric structure.

Findings

Chiral coset geometries from $C^+$-groups are residually connected.

Such geometries are classified as hypertopes.

The result links algebraic group properties to geometric connectedness.

Abstract

We show that a chiral coset geometry constructed from a $C^+$-group necessarily satisfies residual connectedness and is therefore a hypertope.