Abstract

Cholesterics, chiral liquid crystals, typically exhibit a large number of metastable states for a given geometry. This is both a blessing and a curse, it affords great potential for the creation of new devices but can also mean that tight control of a structure can be difficult to achieve. In this talk we will discuss why it is that the tendency of cholesterics to twist means that they have a complex energy landscape. Our principle tools will be drawn from the field of contact topology. By describing cholesterics as contact structures we will show that non-vanishing twist implies conservation of the layer structure in cholesteric liquid crystals. This characterises the morphological richness of these systems, leads to a number of additional topological invariants for cholesteric textures that are not captured by traditional descriptions, 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.