Exotic manifolds in three dimensions

Question

Suppose, we are working in three dimensional setting. Are there any exotic manifolds?(manifolds which are homeomorphic but not diffeomorphic)

Answer 1

It was shown by Edwin Moise in 1952 that any topological 3-manifold has a unique PL and smooth structure. From the beginning of Hatcher's The classification of 3-manifolds (PDF available online):

It was shown by Bing and Moise in the 1950s that every topological 3-manifold can be triangulated as a simplicial complex whose combinatorial type is unique up to subdivision. And every triangulation of a 3-manifold can be taken to be a smooth triangulation in some differential structure on the manifold, unique up to diffeomorphism. Thus every topological 3-manifold has a unique smooth structure, and the classifications up to diffeomorphism and homeomorphism coincide.

EDIT: The following two results are stated and proved in (Moise, 1952), as well as other tame embedding results.

Theorem 3: Every 3-manifold is triangulable.

Theorem 4: If the complexes K1 and K2 are homeomorphic 3-manifolds, then they are combinatorially equivalent (i.e. there exist isomorphic simplicial subdivisions).

E. Moise, 1952. Affine Structures in 3-Manifolds: V. The Triangulation Theorem and Hauptvermutung. The Annals of Mathematics 56 (1), 96-, 1952-07.