Abstract

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

Highlights

  • The concept of a hypertope, introduced recently in [6], is a generalization of an abstract polytope

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

  • Several papers have been written on the subject and in those papers dealing with chiral hypertopes, the check for residual connectedness has been a bit of a struggle

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Summary

Introduction

The concept of a hypertope, introduced recently in [6], is a generalization of an abstract polytope. There are different but equivalent ways to define (abstract) polytopes, one of which being that its faces form a partially ordered set that is a thin, residually connected geometry. This has been generalized in [6] to include structures built from a set of (what we still call) faces that do not form a partially ordered set. There is an easy way to test if a coset geometry is residually connected (see Theorem 3.1). Coset geometries, hypertopes, chirality, C+-groups, residual connectedness

Preliminaries
Hypertopes
Residual connectedness of chiral hypertopes
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