We investigate non-perturbative features of a planar Chern-Simons gauge
theory modeling the long distance physics of quantum Hall systems, including a
finite gap M for excitations. By formulating the model on a lattice, we
identify the relevant topological configurations and their interactions. For M
bigger than a critical value, the model exhibits an oblique confinement phase,
which we identify with Lauglin's incompressible quantum fluid. For M smaller
than the critical value, we obtain a phase transition to a Coulomb phase or a
confinement phase, depending on the value of the electromagnetic coupling.Comment: 8 pages, harvmac, DFUPG 91/94 and MPI-PhT/94-9
