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
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
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
Our book has been reviewed by
Zentralblatt für Mathematik,
Publ. Math. Debrecen,
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).
As mathematical formulae require special treatment in HTML, this part is
contained in a separate document.
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
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 
and Löwen-Polster .
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
is a good source for further information about stable planes and
cf. also Betten-Riesinger 2005.
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.
The list of errata is contained in a
because special precautions are needed to produce mathematical symbols.
Again, the misprints are collected in a
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.
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
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
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
The following home pages may also be of interest: