On the Foundations of Incidence Geometry

Francis Buekenhout and Dominique Buset
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Francis Buekenhout: Univ. Libre de Bruxelles, Serv. de Géom.
Dominique Buset: Univ. Libre de Bruxelles, Serv. de Géom.

A chapter in Geometries and Groups, 1988, pp 269-296 from Springer

Abstract: Abstract The tremendous and sudden development of diagram geometries and related concepts such as chamber systems, combinatorial maps, incidence complexes (see for instance [2], [14], [15], [3]) and their application to finite group theory (see [1], [11], [12]) justifies a careful study of the foundations of the subject, somewhat in the spirit of abstract algebra or general topology, especially since slightly different versions which are more or, less explicitly related to each other by their authors, have flourished. This requires, as usual, an effort towards generality in order to clarify the nature and the interactions of the basic concepts and, at the same time, it requires limitations on the generality, in order to keep close to the status of the subject as it grew recently and in order to preserve the meaning of the foundations.

Keywords: Direct Summand; Finite Rank; Transversal Incidence; Classical Geometry; Sporadic Group (search for similar items in EconPapers)
Date: 1988
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DOI: 10.1007/978-94-009-4017-8_7

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