Compact planes, mostly 8-dimensional. A retrospect

TL;DR

This paper surveys 8-dimensional topological planes, consolidating scattered results, providing new proofs for some theorems, and discussing related geometries of other dimensions.

Contribution

It offers a comprehensive retrospective on 8-dimensional topological planes, including new proofs and updated information since key treatises.

Findings

Consolidation of scattered results on 8-dimensional planes

New proofs for select theorems in the field

Discussion of related geometries in other dimensions

Abstract

Results on $8$-dimensional topological planes are scattered in the literature. It is the aim of the present paper to give a survey of these geometries, in particular of information obtained after the appearance of the treatise Compact Projective Planes or not included in this book. For some theorems new proofs are given and a few related results concerning planes of other dimensions are presented.