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

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 p...

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Bibliographic Details
Published in:Journal of geometry and physics Vol. 180; p. 104614
Main Authors: Thas, Joseph A., Thas, Koen
Format: Journal Article
Language:English
Published: Elsevier B.V 01.10.2022
Subjects:
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Epimorphism
Generalized polygon
Generalized polygon
Cover
Epimorphism
ISSN:0393-0440, 1879-1662
Online Access:Get full text
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Summary: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.
ISSN:0393-0440
1879-1662
DOI:10.1016/j.geomphys.2022.104614