  We derive two types of linearity conditions for mapping class groups of
orientable surfaces: one for once-punctured surface, and the other for closed
surface, respectively. For the once-punctured case, the condition is described
in terms of the action of the mapping class group on the deformation space of
linear representations of the fundamental group of the corresponding closed
surface. For the closed case, the condition is described in terms of the vector
space generated by the isotopy classes of essential simple closed curves on the
corresponding surface. The latter condition also describes the linearity for
the mapping class group of compact orientable surface with boundary, up to
center.
