Handbook of Incidence Geometry - 1st Edition - ISBN: 9780444883551, 9780080533070

Handbook of Incidence Geometry

1st Edition

Buildings and Foundations

Editors: F. Buekenhout
eBook ISBN: 9780080533070
Imprint: North Holland
Published Date: 7th March 1995


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This Handbook deals with the foundations of incidence geometry, in relationship with division rings, rings, algebras, lattices, groups, topology, graphs, logic and its autonomous development from various viewpoints. Projective and affine geometry are covered in various ways. Major classes of rank 2 geometries such as generalized polygons and partial geometries are surveyed extensively.

More than half of the book is devoted to buildings at various levels of generality, including a detailed and original introduction to the subject, a broad study of characterizations in terms of points and lines, applications to algebraic groups, extensions to topological geometry, a survey of results on diagram geometries and nearby generalizations such as matroids.

Table of Contents

An introduction to Incidence Geometry (F. Buekenhout). Projective and affine geometry over division rings (F. Buekenhout, P. Cameron). Foundations of incidence geometry (F. Buekenhout). Projective planes (A. Beutelspacher). Translation planes (M. Kallaher). Dimensional linear spaces (A. Delandtsheer). Projective geometry over a finite field (J.A. Thas). Block designs (A.E. Brouwer, H.A. Wilbrink). Generalized polygons (J.A. Thas). Some classes of rank 2 geometries (F. De Clerck, H. Van Maldeghem). Buildings (R. Scharlau). Point-line spaces related to buildings (A.M. Cohen). Free constructions (M. Funk, K. Strambach). Chain geometries (A. Herzer). Discrete non-Euclidean geometry (J.J. Seidel). Distance preserving transformations (J.A. Lester). Metric Geometry (E.M. Schröder). Pointless geometries (G. Gerla). Geometry over rings (F.D. Veldkamp). Applications of buildings (J. Rohlfs, T.A. Springer). Projective geometry on modular lattices (U. Brehm, M. Greferath, S.E. Schmidt). Finite diagram geometries extending buildings (F. Buekenhout, A. Pasini). Linear topological geometries (T. Grundhöfer, R. Löwen). Topological circle geometries (G.F. Steinke).


© North Holland 1995
North Holland
eBook ISBN:

About the Editor

F. Buekenhout

Affiliations and Expertise

Free University of Brussels, Belgium