  We present an exact scheme of bosonization for anyons (including fermions) in
the two-dimensional manifold of the quantum Hall fluid. This gives every
fractional quantum Hall phase of the electrons one or more dual bosonic
descriptions. For interacting electrons, the statistical transmutation from
anyons to bosons allows us to explicitly derive the microscopic statistical
interaction between the anyons, in the form of the effective two-body and
few-body interactions. This also leads to a number of unexpected topological
phases of the single component bosonic fractional quantum Hall effect that may
be experimentally accessible. Numerical analysis of the energy spectrum and
ground state entanglement properties are carried out for simple examples.
