On contractible open 3-manifolds

Abstract

A contractible open 3-manifold that is not homeomorphic to •3 was first constructed in [12], see also [3 p. 156]. By varying the technique of this construction, an uncountable collection of pairwise nonhomeomorphic contractible open subsets of R 3 was obtained in [8]. Another uncountable collection of pairwise nonhomeomorphic contractible open 3-manifolds, none of which embeds in R 3, was constructed in [6]. An open 3-manifold M is said to be a Whitehead manifold if there is a sequence V~ c M, i = 1, 2 . . . . . of orientable handlebodies satisfying V~ c i n t Vi+l, (1) zq(Vi)--~ rq(Vi+l) is the trivial homomorphism, and (2) M = U V~. (3)