Embeddings in generalized manifolds

We prove that a (2m - n + 1)-connected map f : M-m --> X-n from a compact P L m-manifold M to a generalized n-manifold X with the disjoint disks proper ty, 3m less than or equal to 2n - 2, is homotopic to a tame embedding. Ther e is also a controlled version of this result, as well as a version for non compact M and proper maps f that are properly (2m - n + 1)-connected. The t echniques developed lead to a general position result for arbitrary maps f : M --> X, 3m less than or equal to 2n - 2, and a Whitney trick for separat ing PL submanifolds of X that have intersection number 0, analogous to the well-known results when X is a manifold.