Embedding 3-manifolds and smooth structures of 4-manifolds

Let M be a noncompact 4-manifold with at least two open ends. Suppose that one of these ends is homeomorphic to N × R, where N is an oriented 3-manifold satisfying one of the following conditions: 1. (N) is an extension of the free group by a perfect normal subgroup. 1(N) ≅ Zn1 ⊕…⊕ solZnk, k ⩽ 4, and the link form of N is isomorphic to (1n1)⊕…⊕ (1nk) where each ni, 1 ⩽ i ⩽ k, is a product of primes congruent to 1 (mod 4). H1(N) ≅ Zn1 ⊕ Zn2 and ni (i = 1,2) is a power of a prime congruent to 3 (mod 8). there exist uncountably many different smooth 4-manifolds which are homeomorphic to M.