# Tag Info

If you accept that quantum gravity with matter should be a Topological Quantum Field Theory and that TQFTs probably can't distinguish simply connected homotopy equivalent 4-manifolds, you should come to the conclusion that at least research on quantum gravity would ultimately not depend on the smooth structures of $\mathbb{R}^4$.
There are three facts: existence of uncountably many non-diffeomorphic exotic $\mathbf R^4$'s. any smooth manifold has a PL structure. Any PL manifold of dimension $<7$ has a smooth structure which is unique up to diffeomorphism. For the latter two facts see 1.5 and 1.8 in this survey where explicit references are given.