**Do you know a good reference for the existence and uniqueness of a smooth structure on $3$-manifolds?** As far as I understand topological $3$-manifolds admit a unique smooth structure. I could find the following references for this result: It follows from Hauptvermutung for $3$-manifolds (Theorems 3 and 4 in [2]) and from the fact that a combinatorial $3$-manifold has a unique smoothing (see Theorem 4.2 in [1]). However, I am not quite satisfied with this answer since it requires a good understanding of what is written in these papers. For someone like me, who does not know geometric topology well, it would be better to have a reference to an explicit statement. [1] M. W. Hirsch, B. Mazur, *Smoothings of piecewise linear manifolds.* Annals of Mathematics Studies, No. 80. Princeton University Press, Princeton, N. J.; University of Tokyo Press, Tokyo, 1974. [2] E. E. Moise, Affine structures in 3-manifolds. V. The triangulation theorem and Hauptvermutung. *Ann. of Math.* 56 (1952), 96-114. There is a related post, but I do not find the answer posted there satisfactory. https://mathoverflow.net/questions/83697/smooth-structures-on-closed-3-manifolds-are-unique-up-to-diffeomorphism/83703#83703 I think Moise does not talk about smooth structures only about triangulations.