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DESCRIPTION: In this talk we discuss classical theorems from Convex Geometr
 y such as Carathéodory's Theorem in a more general context of topological d
 rawings of complete graphs. In a (simple) topological drawing the edges of 
 the graph are drawn as simple closed curves such that every pair of edges h
 as at most one common point. Triangles of topological drawings can be viewe
 d as convex sets. This gives a link to convex geometry. Our main result is 
 a generalization of Kirchberger's Theorem that is of purely combinatorial n
 ature. For this we introduce a structure called ''generalized signotopes'' 
 which are a combinatorial generalization of topological drawings. We discus
 s further properties of generalized signotopes. Joint work with Stefan Fels
 ner\, Manfred Scheucher\, Felix Schröder and Raphael Steiner. 
DTSTAMP:20210127T151100
DTSTART:20210208T141500
CLASS:PUBLIC
LOCATION:online
SEQUENCE:0
SUMMARY:Helena Bergold (Fern Universität Hagen): Topological Drawings meet 
 Classical Theorems of Convex Geometry
UID:107739366@www.facetsofcomplexity.de
URL:http://www.facetsofcomplexity.de/monday/20210208-L-Bergold.html
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