Examples of Z-Acyclic and Contractible Vertex-Homogeneous Simplicial Complexes

Abstract

It was shown in [11] that there are no (non-trivial) two- and three-dimensional Z -acyclic vertex-homogeneous simplicial complexes. In this paper we construct a five-dimensional example and further examples in higher dimensions, one of which is Oliver's example of dimension 11, the only previously known example of a non-contractible Z -acyclic vertex-homogeneous simplicial complex. We also present an infinite series of contractible vertex-homogeneous simplicial complexes by starting with one of the Z -acyclic examples.