We have discovered a new mechanism of light guidance, based on a t-PCF with no core [Beravat (2016)]. Cleaving the fibre and examining its cross-section reveals a complete absence of any structure at which light could be trapped. Nevertheless it supports a guided mode: the helical twist creates a topological channel within light is robustly trapped. This arises from the quadratic increase in optical path length with radius (see here), which produces a radial gradient in axial refractive index, creating a potential well within which light is confined by photonic bandgap effects. Using mathematical tools from general relativity [Russell (1999)], we have shown that the geodesics of the light follow closed spiral paths within the topological channel, forming modes that carry OAM. The effective area of these modes decreases with twist rate α, so that by varying the twist rate along the fibre, it would be possible to create fibres whose mode-field diameter changes with position. Unlike in conventional index-guiding fibres, where the guided mode shifts towards the outside of the bend ("normal cornering"), this highly unusual mode shifts inwards towards the bend ("anomalous cornering"). Hamiltonian optics shows that the mode may be viewed as having negative effective mass (caused by the opposite sign of the dispersion surface curvature), so that it moves in the opposite direction when subject to bend forces.