  For each g > 2 and h > 1, we explicitly construct (1) fiber sum
indecomposable relatively minimal genus g Lefschetz fibrations over genus h
surfaces whose monodromies lie in the Torelli group, (2) fiber sum
indecomposable genus g surface bundles over genus h surfaces whose monodromies
are in the Torelli group (provided g > 3), and (3) infinitely many genus g
Lefschetz fibrations over genus h surfaces that are not fiber sums of
holomorphic ones.
