Abstract
We prove that there are uncountably many smooth structures on the four manifold Σ× R if Σ belongs to one of the following classes: 1. rational homology spheres; 2. Seifert 3-manifolds; 3. almost flat 3-manifolds. Moreover, when Σ is a rational homology sphere, these smooth structures on Σ× R can be embedded into the connected sums of CP 2 .
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