**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. [Smooth structures on closed $3$-manifolds are unique up to diffeomorphism?](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.



Unique smooth structure on 3-manifolds
An alternative to Moise's paper for the existence and uniqueness of piecewise linear (PL) structures on topological 3-manifolds is the paper "The triangulation of 3-manifolds" by A.J.S. Hamilton in Quart. J. Math. Oxford (2), 27 (1976), 63-70. The result is stated as Theorem 2 there and proved in the rest of the paper using the famous Kirby torus trick together with several basic results about PL 3-manifolds. 


For the existence and uniqueness of smooth structures on PL 3-manifolds there is a nice exposition in section 3.10 of Thurston's book "Three-Dimensional Geometry and Topology".


