As Carl Brans and others note, it seems too big a coincidence to ignore.

Why is exotic smoothness "good" (in the sense that it permits richer physics or something like that)?

Exotic Smoothness and Physics,*arXiv*

"there are an infinity of differentiable structures on topological R4, no two of which are equivalent, i.e., diffeomorphic, to each other... The fact that R4Θ’s arise only in the physically significant case of dimension four makes the result even more intriguing to physicists..."

*Exotic Smoothness and Physics: Differential Topology and Spacetime Models*, book