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F. Buekenhout, "Handbook of Incidence Geometry: Buildings and Foundations"

Book Description

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.

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. Schr?der). 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. Grundh?fer, R. L?wen). Topological circle geometries (G.F. Steinke).

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