On the isomorphism types of Moebius-Kantor complexes (Q2278150)

A Moebius-Kantor complex is a 2-complex with triangle faces, whose links are isomorphic to the Moebius-Kantor graph. In this paper, the authors continue their investigations of these complexes, which was begun in [``Intermediate rank and property RD'', Preprint, \url{arXiv:0710.1514}]. They study the isomorphism type of simply connected Moebius-Kantor complexes, and aim to prove that (a) there are infinitely many isomorphism types with a cocompact automorphism group, (b) there are uncountably many isomorphism types, in general. They use a local invariant for Moebius-Kantor complexes called the parity and show that the parity can be computed explicitly in certain constructions.