2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/223560We 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.This is the version published by Geometry & Topology Monographs on 22 April 2006Geometric TopologyAlgebraic Topology57R67, 18F25text