Embeddings in generalized manifolds

J. L. Bryant and W. Mio

We prove that a (2m-n+1)-connected map f:M --> X from a compact piecewise-linear m-manifold M to a generalized n-manifold X with the disjoint disks property, 3m =< 2n-2, is homotopic to a tame embedding. There is also a controlled version of this result, as well as a version for noncompact M and proper maps f that are properly (2m-n+1)-connected. The techniques developed lead to a general position result for arbitrary maps f:M --> X, 3m =< 2n-2, and a Whitney trick for separating PL submanifolds of X that have intersection number 0, analogous to the well-known results when X is a manifold.