Flag-homogeneous compact connected polygons. II (Q1591211)

The paper provides an explicit classification of all flag-homogeneous compact connected polygons. These are precisely the compact connected Moufang polygons. This result extends the results obtained by the same authors in Part I [Geom. Dedicata 55, No. 1, 95-114 (1995; Zbl 0840.51009)]. There flag-homogeneous compact connected polygons with equal topological parameters are considered. So the paper under review focuses on the remaining cases, namely compact connected quadrangles with different topological parameters. Topologically these cases are rather different from the cases with equal topological parameters. For example, the Euler characteristic of the spaces under consideration is zero or the fundamental group of the flag space is infinite. This makes new techniques necessary. The possible combinations of topological parameters split into four classes, each of which requires different, rather tedious arguments.