  Recent calculations of the edge tunneling exponents in quantum Hall states
appear to contradict their topological nature. We revisit this issue and find
no fundamental discrepancies. In a microscopic model of fractional quantum Hall
liquids with electron-electron interaction and confinement, we calculate the
edge Green's function via exact diagonalization. Our results for $\nu = 1/3$
and 2/3 suggest that in the presence of Coulomb interaction, the sharpness of
the edge and the strength of the edge confining potential, which can lead to
edge reconstruction, are the parameters that are relevant to the universality
of the electron tunneling I-V exponent.
