  We demonstrate that integrable abelian vortex equations on constant curvature
Riemann surfaces can be reinterpreted as flat non-abelian Cartan connections.
By lifting to three dimensional group manifolds we find higher dimensional
analogues of vortices. These vortex configurations are also encoded in a Cartan
connection. We give examples of different types of vortex that can be
interpreted this way, and compare and contrast this Cartan representation of a
vortex with the symmetric instanton representation.
