Duality in Multi-layered Quantum Hall Systems

The braid group dynamics captures the fractional quantum Hall effect (FQHE) as a manifestation of puncture phase. When the dynamics is generalized for particles on a multi-sheeted surface, we obtain new tools which determine the fractional charges, the quantum statistics, and the filling factors of the multi-layered FQHE. A many-quasihole wavefunction is proposed for the bilayered samples. We also predict a ν = 5/7 FQHE for triple-layered samples. The viability of 3-dimensional FQHE and the application of the concept of generalized duality to anyonic superconductivity are discussed.