Resonant cavities are essential building blocks governing many wave based phenomena, and, their geometry together with reciprocity, fundamentally limit the integration of optical devices. Topological lasing has been proposed in two dimensions using arrays of ring resonators with no time-reversal symmetry breaking, and in one-dimensional lattice of polariton micropillars. However, these systems cannot implement cavities of arbitrary shapes due to their preserved time-reversal symmetry. An elusive, but fundamental, implication of topology is the existence of a new class of geometry-independent photonic components. For example, the possibility to construct geometry-independent cavities opens a new paradigm in cavity quantum electro dynamics and photonic integration, as, it enables denser packing of components and sources of arbitrary form-factors. This prospect will alleviate the otherwise stringent constraints to use preset cavities that leave much chip space unused. Topology also naturally addresses the pressing need for non-reciprocal components that protect sources against back scattering.