Does a noncompact, simply connected 6-manifold have a unique smooth structure? Maybe with more assumptions like having torsion-free homology and being spin?
Note that in the compact case C.T.C. Wall showed that this is true. Can counterexamples be constructed with exotic $\mathbb{R}^4$s, e.g. $X\times S^2$ with $X$ an exotic $\mathbb{R}^4$?
Any related references would be appreciated.