Adiabatic Transport of Geometric Singularities in the Quantum Hall Effect

We present a framework for studying the fractional Quantum Hall Effect (FQHE) on singular surfaces - in particular surfaces with multiple geometric singularities. It is now known that, aside from the Hall conductance and viscosity, there exists a third universal transport coefficient of the FQHE - the gravitational anomaly. This coefficient is difficult to measure since it usually appears as a higher order correction to observable quantities, such as the particle density. Singular surfaces are the first setting where the gravitational anomaly appears as a leading order effect. These surfaces are therefore ideal for studying geometric response and the gravitational anomaly within the FQHE. We expand the generating functional in the large $N$ limit on such surfaces. From there, we braid the conical singularities of the surface and find a remarkable result - the gravitational anomaly determines the braiding statistics of the transported conical singularities.