H. Salzmann et al.: Compact Projective Planes

cover CPP

Walter de Gruyter, Berlin - New York 1995

ISSN 0938-6572

ISBN 3-11-011480-1

This page provides links to reviews about the book "Compact Projective Planes", and comments on recent developments of the topics treated. We also give some hints to related fields (mainly, compact generalized polygons and stable planes) and to home pages of some people doing research in these fields. You may find information about the authors, and lists of errata and misprints. If you think you found any error in the book, feel free to contact any of the authors.

If you want to order the book (or get information about its price or availability): use this link to the pages of W. de Gruyter.

You may also have a look at the table of contents, or at the preface.

References to the book will be made in the form [CPP: XX.YY] or [CPP: p.ZZZ], where XX.YY is the number of the respective result, or ZZZ is a page number. We also give references to recently published articles; bibliographic data is contained in a list of recent literature. References to that list will be made by quoting author and year of publication.

Reviews:

Our book has been reviewed by
Zentralblatt für Mathematik,
Mathematical Reviews,
Publ. Math. Debrecen,
Choice,
Monatshefte für Mathematik 124 p.281,
L'Enseignement Mathématique 42 p.26,
Jahresber. DMV 100 pp.53-55.

Click the name of the journal to follow a link to that journal (or to the review, if available).

Recent developments:

As mathematical formulae require special treatment in HTML, this part is contained in a separate document.

Related fields:

Generalized polygons:

Projective planes form a special case of generalized polygons (or spherical Tits buildings of rank 2); namely, they are exactly the generalized triangles. A structure theory in the spirit of CPP for compact connected generalized n-gons for n>3 is presently evolving; compare Knarr [1990], Kramer [1994], Schroth [1995], Grundhöfer-Knarr-Kramer [1995], Grundhöfer-Knarr-Kramer [1998], Stroppel-Stroppel [1999], Joswig [2000], Stroppel [2002], Kramer [2002], Rosehr [2005b].

Stable planes:

The study of actions of groups of automorphisms of compact projective planes frequently leads to the consideration of the geometry induced on some open set of points. These geometries are examples of stable planes (most prominent are the classical affine and hyperbolic planes); there do exist stable planes that do not admit any embedding as an open subplane of a projective plane. See also Polster-Steinke [2001] and Löwen-Polster [2005].

Topological linear incidence geometries:

While stable planes are planar objects (this is the effect of the stability axiom requiring that the set of pairs of intersecting lines is open in the space of all pairs of lines), there is also the notion of stable spaces. According to a result due to H. Groh, every (sufficiently rich) stable space which is not a stable plane can be embedded in a desarguesian topological projective space, over some topological (skew) field.
The survey article Grundhöfer-Löwen 1995 is a good source for further information about stable planes and stable spaces; cf. also Betten-Riesinger 2005.

Topological unitals:

Unitals are a well established area of interest in finite geometry. Classical examples occur as the geometries induced on sets of absolute points of polarities. It is not yet clear what the general definition of unital in a compact projective plane should be. It appears that the definition should include that the point set is a sphere, and the blocks are spheres of some fixe dimension.

Errata:

The list of errata is contained in a separate file because special precautions are needed to produce mathematical symbols.

Misprints:

Again, the misprints are collected in a separate file.

The Authors:

You can reach the authors by email. (In order to avoid as much spam mail as possible, the addresses are given in a form that is still easily readable for humans, but not for machines: put an AT sign between the name and the institution. Sorry for any inconvenience this may cause.) Click the names to follow links to personal home pages.

Helmut Salzmann	helmut.salzmann	uni-tuebingen.de
Dieter Betten	betten	math.uni-kiel.de
Theo Grundhöfer	grundhoefer	mathematik.uni-wuerzburg.de
Hermann Hähl	haehl	igt.uni-stuttgart.de
Rainer Löwen	r.loewen	tu-bs.de
Markus Stroppel	stroppel	igt.uni-stuttgart.de

You may also see several pictures of the authors (click onto the small pictures to load big versions):

First, the authors on a duty call to C.F. Gauss and the regular 17-gon.

(From left to right: R. Löwen, H. Salzmann, H.Hähl, D. Betten, T. Grundhöfer, M. Stroppel. Above them all: C.F. Gauss.)

Having a break at the Hermann Hankel Zimmer at Tübingen.
(Left to right: H.Hähl, D. Betten, T. Grundhöfer, H. Salzmann, M. Stroppel, R. Löwen.)

Finally, the pleasure of holding the first copy in one's hands!

The formal clothing is due to the fact that this picture was taken at the celebration of H. Salzmann's 65th birthday. Left to right, you see T. Grundhöfer, M. Stroppel, D. Betten, H. Salzmann, R. Löwen, and H.Hähl.

The following home pages may also be of interest:
Linus Kramer, Burkard Polster.