We develop an epsilon-controlled algebraic L–theory, extending our earlier work on
epsilon-controlled algebraic K–theory. The controlled L–theory is very close to
being a generalized homology theory; we study analogues of the homology
exact sequence of a pair, excision properties, and the Mayer–Vietoris exact
sequence. As an application we give a controlled L–theory proof of the classic
theorem of Novikov on the topological invariance of the rational Pontrjagin
classes.
