Embeddings of non-simply-connected 4-manifolds in 7-space. II. On the smooth classification

Abstract

We work in the smooth category. Let be a closed connected orientable 4-manifold with torsion free, where. Our main result is a readily calculable classification of embeddings up to isotopy, with an indeterminacy. Such a classification was only known before for by our earlier work from 2008. Our classification is complete when or when the signature of is divisible neither by 64 nor by 9. The group of knots acts on the set of embeddings up to isotopy by embedded connected sum. In Part I we classified the quotient of this action. The main novelty of this paper is the description of this action for, with an indeterminacy. Besides the invariants of Part I, detecting the action of knots involves a..