  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.

Soft Condensed Matter