  We study the action of the mapping class group on the real homology of finite
covers of a topological surface. We use the homological representation of the
mapping class to construct a faithful infinite-dimensional representation of
the mapping class group. We show that this representation detects the
Nielsen-Thurston classification of each mapping class. We then discuss some
examples that occur in the theory of braid groups and develop an analogous
theory for automorphisms of free groups. We close with some open problems.
