  Using tools and concepts from contact topology we show that non-vanishing
twist implies conservation of the layer structure in cholesteric liquid
crystals. This leads to a number of additional topological invariants for
cholesteric textures, such as layer numbers, that are not captured by
traditional descriptions, characterises the nature and size of the chiral
energy barriers between metastable configurations, and gives a geometric
characterisation of cholesteric dynamics in any context, including active
systems, those in confined geometries or under the influence of an external
field.
