Papers › Small Triangulations of $4$-Manifolds: Introducing the $4$-Manifold Census
Small Triangulations of $4$-Manifolds: Introducing the $4$-Manifold Census
Rhuaidi Antonio Burke, Benjamin A. Burton, Jonathan Spreer
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We present a framework to classify PL-types of large censuses of triangulated $4$-manifolds, which we use to classify the PL-types of all triangulated $4$-manifolds with up to six pentachora. This is successful except for triangulations homeomorphic to the $4$-sphere, ℂP², and the rational homology sphere QS⁴(2), where we find at most four, three, and two PL-types respectively. We conjecture that they are all standard. In addition, we look at the cases resisting classification and discuss the combinatorial structure of these triangulations -- which we deem interesting in their own rights.
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