The triangle groups (2,4,5) and (2,5,5) are not systolic

Annette Karrer; Koen Struyve; Petra Schwer

The triangle groups (2,4,5) and (2,5,5) are not systolic

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arxiv 1812.08567 v2 pith:TDLMYKQN submitted 2018-12-20 math.GR math.CO

Annette Karrer , Petra Schwer , Koen Struyve This is my paper

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keywords groupssystolictrianglealongcomplexesexampleshyperbolicinvolutions

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abstract

In this paper we provide new examples of hyperbolic but nonsystolic groups by showing that the triangle groups $(2,4,5)$ and $(2,5,5)$ are not systolic. Along the way we prove some results about subsets of systolic complexes stable under involutions.

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Proves geometric actions on weakly modular graphs for tilde A_n Coxeter groups via canonical embeddings into R^{n+1} and extends the result to tilde A_3 buildings.

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