Controlled L-theory

Abstract

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.

This is the version published by Geometry & Topology Monographs on 22 April 2006

References in corpus (1)

• Stability in controlled L-theory

Cited by in corpus (7)

• Stability in controlled L-theory
• Controlled homotopy equivalences and structure sets of manifolds
• The quadratic form E_8 and exotic homology manifolds
• Topological Bordism of Singular Spaces and an Application to Stratified L-Classes
• Some recent approaches in 4-dimensional surgery theory
• On the construction and topological invariance of the Pontryagin classes
• Limits of manifolds in the Gromov-Hausdorff metric space