Combinatorial 8-Manifolds having Cohomology of the Quaternionic Projective Plane and Their Nonembeddings

Abstract

In this paper we prove, that none of the three combinatorial 8- manifolds on 15 vertices constructed by Brehm and Kuhnel, each of which is a cohomology quaternionic projective plane, can be combinatorially embedded in the Euclidean 12-space, though they have tight polyhedral embeddings in Euclidean 14-space. This extends a similar method already known for the nonembeddings of real and complex projective planes.