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Rotation groups virtually embed into right-angled rotation groups

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arxiv 2404.15652 v1 pith:KSITAELR submitted 2024-04-24 math.GR math.MG

Anthony Genevois This is my paper · ORCID
classification math.GRmath.MG
keywords groupsrotationright-angledcoxeterembedvirtuallygraphproducts
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It is a theorem due to F. Haglund and D. Wise that reflection groups (aka Coxeter groups) virtually embed into right-angled reflection groups (aka right-angled Coxeter groups). In this article, we generalise this observation to rotation groups, which can be thought of as a common generalisation of Coxeter groups and graph products of groups. More precisely, we prove that rotation groups (aka periagroups) virtually embed into right-angled rotation groups (aka graph products of groups).

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  1. Cell structure of mediangle graphs

    math.CO 2025-05 conditional novelty 7.0 of 10

    Every bipartite mediangle graph is the tope graph of a finitary complex of oriented matroids, so it carries a contractible cell complex with simplicial oriented matroid cells.

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