Related papers: Chirality in incidence geometry
We study incidence geometries that are thin and residually connected. These geometries generalise abstract polytopes. In this generalised setting, guided by the ideas from the polytopes theory, we introduce the concept of chirality, a…
A generalization of incidence relations in abstract polytope has been explored, and parameterized surfaces are used as primers. The abstract orientable incidence structure is defined as an algebraic model of incidence relations, in which…
The aim of this paper is to use the framework of incidence geometry to develop a theory that permits to model both the inner and outer automorphisms of a group G simultaneously. More precisely, to any group G, we attempt to associate an…
In this paper we give group-theoretical conditions on the maximal parabolic subgroups of a coset geometry for it to be a chiral hypertope, bypassing the need to construct the incidence graph of the coset geometry to determine whether or not…
Regular incidence complexes are combinatorial incidence structures generalizing regular convex polytopes, regular complex polytopes, various types of incidence geometries, and many other highly symmetric objects. The special case of…
This paper presents a technique for constructing new chiral or regular polyhedra (or maps) from self-dual abstract chiral polytopes of rank 4. From improperly self-dual chiral polytopes we derive "Petrie-Coxeter-type" polyhedra (abstract…
We show that a chiral coset geometry constructed from a $C^+$-group necessarily satisfies residual connectedness and is therefore a hypertope.
Chirality is one of the important assymmetrical property in wide area of natural science, which has been studied to predict molecular behavior. One of good methods to analyze molecules with complex structures is representing them as graphs…
The paper surveys highlights of the ongoing program to classify discrete polyhedral structures in Euclidean 3-space by distinguished transitivity properties of their symmetry groups, focussing in particular on various aspects of the…
An abstract polytope of rank n is said to be chiral if its automorphism group has two orbits on the flags, such that adjacent flags belong to distinct orbits. Examples of chiral polytopes have been difficult to find. A "mixing" construction…
This paper makes some preliminary observations towards an extension of current work on graphs defined on groups to simplicial complexes. I define a variety of simplicial complexes on a group which are preserved by automorphisms of the…
In this letter we uncover a new facet of chiral symmetry and the implications of its breaking in some theories. By generalizing the concept of chiral symmetry, tensor theories naturally arise. This novel approach adds to the known uses of…
General features of microscopic and macroscopic chiral structures can be discussed under the standard of orthogonal group theory. Configuration space of systems, not physical space, is taken into account. This change of perspective allows…
Coset incidence geometries, introduced by Jacques Tits, provide a versatile framework for studying the interplay between group theory and geometry. In this article, we build upon that idea by extending classical group-theoretic…
The present paper is a continuation of our work on curved finitary spacetime sheaves of incidence algebras and treats the latter along Cech cohomological lines. In particular, we entertain the possibility of constructing a non-trivial de…
Molecular chirality is actively researched in a variety of areas of biology, including biochemistry, physiology, pharmacology, etc., and today many chiral compounds are widely known to exhibit biological properties. The molecular structure…
Triality is a classical notion in geometry that arose in the context of the Lie groups of type $D_4$. Another notion of triality, Wilson triality, appears in the context of reflexible maps. We build a bridge between these two notions,…
A lemma of Tits establishes a connection between the simple connectivity of an incidence geometry and the universal completion of an amalgam induced by a sufficiently transitive group of automorphisms of that geometry. In the present paper,…
In this paper, we investigate automorphisms of compact K\"ahler manifolds with different levels of topological triviality. In particular, we provide several examples of smooth complex projective surfaces X whose groups of…
The aim of these notes is to present an accessible overview of some topics in classical algebraic geometry which have applications to aspects of discrete integrable systems. Precisely, we focus on surface theory on the algebraic geometry…