Controlled algebra and the novikov conjectures for K- and L-theory

Abstract

IN THIS paper we combine the methods of [S] with the continuously controlled algebra of [l] and the L-theory of additive categories with involution [22] to split assembly maps in Kand L-theory. Specifically, we prove the following theorems. Let I be a group with finite classifying space BT. Assume ET admits a compactification X (meaning X compact, and ET is an open dense subset) satisfying the following conditions, (denoting X ET by Y).