2026-08-06T21:55:49Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:23180 2025-10-02T12:42:08Z ddc:004 open_access

Small Triangulations of 4-Manifolds and the 4-Manifold Census Burke, Rhuaidi Antonio Burton, Benjamin A. Spreer, Jonathan computational low-dimensional topology triangulations census of triangulations 4-manifolds PL standard 4-sphere Pachner graph mathematical software experiments in low-dimensional topology 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 6 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Rhuaidi Antonio Burke and Benjamin A. Burton and Jonathan Spreer 2025 Is Part Of LIPIcs, Volume 332, 41st International Symposium on Computational Geometry (SoCG 2025) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.SoCG.2025.28 urn:nbn:de:0030-drops-231805 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2025.28 eng https://creativecommons.org/licenses/by/4.0/legalcode