One of the distinguishing features of the topological category is the following periodicity in the set of homotopy TOP structures on X.
THEOREM (Siebenmann). Let Xm, m ≦ 5, be a connected compact topological manifold with non-empty boundary. Then
It was conjectured by Siebenmann (see , p. 283) that the analogous periodicity should also exist for noncompact manifolds.
The purpose of this paper is to prove that this is indeed the case, namely:
THEOREM 1. Let Let Xm, m ≦ 6, be a connected noncompact topological manifold with non-empty boundary. Then