For compact simply-connected manifolds of dimension 4 Simon Donaldson found examples with an infinite number of inequivalent PL structures, and Michael Freedman found the E8 manifold which not only has no PL structure, but is not even homeomorphic to a simplicial complex.
Riemannian manifold | manifold | Manifold | Differentiable manifold | 4-manifold | Stein manifold | Simplicial manifold | Riemann manifold | Piecewise linear manifold | Manifold Trilogy | Leek and Manifold Valley Light Railway | Finsler manifold | E8 manifold | Complex manifold | complex manifold | closed manifold | 3-manifold |