  An adiabatic approach put forward by Greiter and Wilczek interpolates between
the integer quantum Hall effects of electrons and composite fermions by varying
the statistical flux bound to electrons continuously from zero to an even
integer number of flux quanta, such that the intermediate states represent
anyons in an external magnetic field with the same "effective" integer filling
factor. We consider such anyons on a torus, and construct representative wave
functions for their ground as well as excited states. These wave functions
involve higher Landau levels in general, but can be explicitly projected into
the lowest Landau level for many parameters. We calculate the variational
energy gap between the first excited state and ground state and find that it
remains open as the statistical phase is varied. Finally, we obtain from these
wave functions, both analytically and numerically, various topological
quantities, such as ground-state degeneracy, the Chern number, and the Hall
viscosity.
