Compact Polygons

2001/04/05 by Linus Kramer, Kramer, Linus
Mathematics · #51H 57P 51E #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #math.DG #math.GT #msc:51E #msc:51H #msc:57P

paper · pdf · doi:10.48550/arxiv.math/0104064

arxiv created 2001/04/05 · arxiv updated 2009/11/30

Abstract

We develop the basic topological properties of compact polygons, i.e. of compact topological Tits buildings of rank two. It is proved that the Coxeter diagram of such a building is always crystallographic, that is, compact connected n-gons exist only for n=3,4,6. We classify compact polygons which admit a transitive group action, showing that such a polygon is Moufang and thus related to a real Lie group of rank 2.

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