L-compactifications of open manifolds

Suppose an open n-manifold M-n may be compactified to an ANR <(M-n)over cap > so that <(M-n)over cap> - M-n is a L-set in <(M-n)over cap>. It is shown that (when n greater than or equal to 5) the double of <(M-n)over bar> alon g its "L-boundary" is an n-manifold. More generally, if M-n and N-n each ad mit compactifications with homeomorphic L-boundaries, then their union alon g this common boundary is an n-manifold. This result is used to show that i n many cases L-compactifiable manifolds are determined by their S-boundarie s. For example, contractible open n-manifoids with homeomorphic I-boundarie s are homeomorphic. As an application, some special cases of a weak Borel c onjecture are verified. Specifically, it is shown that closed aspherical n- manifolds (n not equal 4) having isomorphic fundamental groups which are ei ther word hyperbolic or CAT(0) have homeomorphic universal covers. (C) 1999 Elsevier Science Ltd. All rights reserved.