Examples of \(\mathbb{Z}\)-acyclic and contractible vertex-homogeneous simplicial complexes
This paper constructs examples of \(\mathbb Z\)-acyclic vertex-homogeneous simplicial complexes. A primary motivation for this work is the Evasiveness Conjecture for simplicial complexes, which conjectures that the only non-evasive vertex-homogeneous simplicial complexes are simplices. (Non-evasiveness is a stronger property than acyclicity.) One such example, in dimension 11, was first found by Bob Oliver. The current paper finds 7 such examples, one of them in dimension 5, by constructions arising from the spherical dodecahedron space. These examples are the starting point for infinite families of such complexes.
scientific article; zbMATH DE number 1743171