Abstract: In this article we prove that the surgery groups of the fundamental group of several classes of Haken 3-manifolds can be computed in terms of a generalized homology theory even if the manifolds do not support any nonpositively curved Riemannian metric. (For nonpositively curved Riemannian manifolds (any dimension) this result is the Farrell-Jones Topological Rigidity Theorem.) This class of manifolds (properly) contains all irreducible 3-manifolds with nonempty boundary. This also implies that the Integral Novikov Conjecture is true for the fundamental groups of these manifolds.
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