Handbook of incidence geometry : buildings and foundations
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
1 online resource (xi, 1420 pages) : illustrations
9780444883551, 044488355X
162589397
1. An introduction to incidence geometry / F. Buekenhout
2. Projective and affine geometry over division rings / F. Buekenhout and P. Cameron
3. Foundations of incidence geometry / F. Buekenhout
4. Projective planes / A. Beutelspacher
5. Translation planes / M. Kallaher
6. Dimensional linear spaces / A. Delandtsheer
7. Projective geometry over a finite field / J. A. Thas
8. Block designs / A. E. Brouwer and H. A. Wilbrink
9. Generalized polygons / J. A. Thas
10. Some classes of rank 2 geometries / F. De Clerck and H. Van Maldeghem
11. Buildings / R. Scharlau
12. Point-line spaces related to buildings / A. M. Cohen
13. Free constructions / M. Funk and K. Strambach
14. Chain geometries / A. Herzer
15. Discrete non-Euclidean geometry / J. J. Seidel
16. Distance preserving transformations / J. A. Lester
17. Metric geometry / E. M. Schroder
18. Pointless geometries / G. Gerla
19. Geometry over rings / F. D. Veldkamp. 20. Applications of buildings / J. Rohlfs and T. A. Springer
21. Projective geometry on modular lattices / U. Brehm, M. Greferath and S. E. Schmidt
22. Finite diagram geometries extending buildings / F. Buekenhout and A. Pasini
23. Linear topological geometries / T. Grundhofer and R. Lowen
24. Topological circle geometries / G. F. Steinke
Electronic reproduction, [Place of publication not identified], HathiTrust Digital Library, 2010