Controlled L-theory

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.