Transversality in generalized manifolds

Suppose that X is a generalized n-manifold, n greater than or equal to 5, satisfying the disjoint disks property, and M and Q are topological m- and q-manifolds, respectively, 1-LCC embedded in X, with n - m greater than or equal to 3 and n - q greater than or equal to 3. We define what it means for M to be stably transverse to Q in X. In the metastable range, 3m less than or equal to 2(n - 1) and 3(m + q) < 4(n - 1), we show that there is an arbitrarily small homotopy of M to a 1-LCC embedding that is stably transverse to Q. (C) 1999 Elsevier Science B.V. All rights reserved.