A new framework classifies PL-types for every triangulated 4-manifold with up to six pentachora, succeeding except on the 4-sphere, CP^2 and QS^4(2) where at most four, three and two types appear respectively.
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Small Triangulations of $4$-Manifolds: Introducing the $4$-Manifold Census
A new framework classifies PL-types for every triangulated 4-manifold with up to six pentachora, succeeding except on the 4-sphere, CP^2 and QS^4(2) where at most four, three and two types appear respectively.