報告題目:Abstract regular polytopes whose automorphism groups are alternating groups

報告時間:2019年5月20日10:00-11:00

報告地點:特立南203

邀請人:陳靜

報告人:比利時自由大學Dimitri教授。

報告摘要: Abstract polytopes are a generalization of the classical notion of convex geometric polytopes to more general structures. The highly symmetric examples are the most studied. They include not only classical regular polytopes such as the Platonic solids, but also non-degenerate regular maps on surfaces.We prove that for any integer n > 11, and for every r in the interval [3, …,Floor( (n-1)/2 )], the group Alt(n) is the automorphism group of at least one abstract regular polytope of rank r therefore showing that the only alternating group whose set of ranks is not an interval is Alt(11).


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