Tag Info

New answers tagged


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.

Top 50 recent answers are included