Nematics, Knots and Non-orientable Surfaces

TL;DR

This paper explores the topological properties of liquid crystal defects induced by colloids representing non-orientable surfaces, enabling the construction of complex knots and links such as torus knots around Möbius strips.

Contribution

It extends previous work by analyzing the topological implications of colloids with non-orientable surfaces and demonstrates how to create intricate knotted configurations in liquid crystals.

Findings

Topological analysis of colloids with non-orientable surfaces.

Construction of torus knots and links around Möbius strips.

Potential applications in photonic device development.

Abstract

Knots and knotted fields enrich physical phenomena ranging from DNA and molecular chemistry to the vortices of fluid flows and textures of ordered media. Liquid crystals provide an ideal setting for exploring such topological phenomena through control of their characteristic defects. The use of colloids in generating defects and knotted configurations in liquid crystals has been demonstrated for spherical and toroidal particles and shows promise for the development of novel photonic devices. Extending this existing work, we describe the full topological implications of colloids representing non-orientable surfaces and use it to construct torus knots and links of type ($p$,2) around multiply-twisted M\"obius strips.