Epimorphisms of generalized polygons A: The planes, quadrangles and hexagons

Abstract

Inspired by a theorem by Skornjakov–Hughes–Pasini [8,5,6] and a problem which turned up in our recent paper [11], we start a study of epimorphisms with source a thick generalized m-gon and target a thin generalized m-gon. In this first part of the series, we classify the cases m=3,4 and 6 when the polygons are finite. Then we show that the infinite case is very different, and construct examples which strongly deviate from the finite case. A number of general structure theorems are also obtained. We introduce the theory of locally finitely generated generalized polygons and locally finitely chained generalized polygons along the way.