Compact projective planes. With an introduction to octonion geometry
type: Item
instance of: scholarly article
title: Compact projective planes. With an introduction to octonion geometry
zbMATH Open document ID: 0851.51003
author: Dieter Betten
author: Helmut Salzmann
author: Theo Grundhöfer
author: Hermann Hähl
author: Rainer Löwen
author: Markus Stroppel
published in: De Gruyter Expositions in Mathematics
publication date: 1996-04-24T00:00:00Z
review text: A topological projective plane is a projective plane \({\mathcal P} = (P,{\mathcal L})\) in which the point set \(P\) and the set of lines \(\mathcal L\) are equipped with topologies that are neither discrete nor indiscrete such that the geometric operations of joining two points by a line and of intersecting two lines in a point are continuous on their domains of definition. One calls such a topological projective plane (locally) compact, connected or \(n\)-dimensional if the point space has the respective property. The study of topological projective planes involves tools and techniques from many different areas of mathematics and the book gives an excellent illustration of their interplay. The study of compact, connected topological projective planes was initiated in the early 1950s by H. Salzmann. Since then many beautiful and deep results have been achieved by an ever growing number of researchers in this area. In particular, 2- and 4-dimensional planes are now well understood and the theory of 8- and 16-dimensional planes is rapidly developing. However, the results are scattered in the literature. In that this book gives a systematic account of most of these results it has been long waited for. The book provides a wealth of information and should prove an extremely useful text both as an introduction to compact, connected topological projective planes as well as a valuable and convenient reference and a sound foundation for future investigations. It gives an up-to-date picture incorporating unpublished results but also including simplified proofs and proofs of folklore. The book is a highly readable, self-contained monograph. It serves as an excellent advertisement for topological geometry and will attract many more mathematicians to this area. Various chapters may appeal to the interested broader mathematical community. In particular, those who are interested in topology and the theory of Lie groups and their interactions in other disciplines may consult the …
reviewed by: Günter F. Steinke
Mathematics Subject Classification ID: 51-02
Mathematics Subject Classification ID: 51H10
Mathematics Subject Classification ID: 51H25
Mathematics Subject Classification ID: 51A40
Mathematics Subject Classification ID: 51N30
zbMATH DE Number: 870319
zbMATH Keywords: classical projective plane
zbMATH Keywords: translation plane
zbMATH Keywords: topological projective plane
zbMATH Keywords: projective plane
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 870319