04. Juni 2026
Wacław Marzantowicz (Adam Mickiewicz University Poznań)
Vertex-minimal triangulations of spaces with a given fundamental group and a progress in the Björner-Lutz conjecture on minimal triangulations of the Poincare sphere
The number of non-isomorphic simplicial complexes with up to n vertices increases super-exponentially with n. We provide a complete list of groups that arise as fundamental groups of simplicial complexes with at most 8 vertices. In addition we give many examples of fundamental groups of complexes with 9 vertices. Our results lead to many applications, including progress on the Björner–Lutz conjecture regarding vertex-minimal triangulations of the Poincaré homology sphere, improved recognition criteria for PL triangulations of manifolds and computation of the Karoubi–Weibel invariant for many groups.