On geometric delusions of hexagonal structures

TL;DR

This paper explores the topological and geometric effects in hexagonal 2D structures, linking curvature, gauge fields, and stability, and introduces a novel theoretical framework for understanding these phenomena.

Contribution

It presents a new theoretical perspective on how topological delusions influence the geometry and stability of hexagonal structures in 2D fermionic systems.

Findings

Topological invariants relate to geometric distortions in hexagonal lattices.

Curvature effects can be interpreted through effective gauge fields.

Theoretical description of structure stability based on topological considerations.

Abstract

The confining geometries of fermions in 2D structures exhibits interesting results that have highest symmetry. Delusion can be considered as the topological effect which is topological invariant. Topologically, genus zero surfaces needs excess of pentagons while in surfaces g>2 surfaces needs excess of heptagons. The curvature effect and the rise of effective gauge field can be interpreted from delusion effects in hexagonal lattice. This idea is novel in its scope as it can state theoretical description of structures and their stability.