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arXiv · 2201.03901

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

Joseph A. Thas·Koen Thas
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Abstract

Inspired by a theorem by Skornjakov-Hughes-Pasini [9, 7, 8] and a problem which turned up in our recent paper [13], 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.

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Joseph A. Thas, Koen Thas. 2022-01-11. Epimorphisms of generalized polygons A: The planes, quadrangles and hexagons. https://doi.org/10.1016/j.geomphys.2022.104614

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