ABSTRACT

Spreadsets represent a matrix-based approach to the study of spreads and hence translation planes. Moreover, spreadsets have proven to be particu­ larly effective in the study of finite translation planes. In fact, their growing use during the 1970’s has led to a transformation of the entire field of finite translation planes. Whereas before this period the known classes of trans­ lation planes were quite restricted, by the early 1980’s, the application of spreadset-based methods led to an explosive and arguably unmanageable growth in the known classes of finite spreads. It became evident that finite translation planes are too numerous to classify up to isomorphism. On the other hand, we do try for a classification of sorts in the Atlas where we bring to bear various construction devices that classify a plane by its lineage.