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Embedding products of trees into higher rank

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arxiv 2405.02226 v1 pith:OVETIZW7 submitted 2024-05-03 math.GR math.MG

Oussama Bensaid , Thang Nguyen This is my paper · ORCID
classification math.GRmath.MG
keywords embeddingrankcopiesexistsmathbbproductresultthere
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abstract

We show that there exists a quasi-isometric embedding of the product of $n$ copies of $\mathbb{H}_{\mathbb{R}}^2$ into any symmetric space of non-compact type of rank $n$, and there exists a bi-Lipschitz embedding of the product of $n$ copies of the $3$-regular tree $T_3$ into any thick Euclidean building of rank $n$ with co-compact affine Weyl group. This extends a previous result of Fisher--Whyte. The proof is purely geometrical, and the result also applies to the non Bruhat--Tits buildings.

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  1. Topological expanders, coarse geometry and thick embeddings of complexes

    math.MG 2024-11 conditional novelty 8.0 of 10

    Topological overlap profiles are introduced as higher-dimensional analogues of the separation profile, with new calculations and coarse geometric obstructions.

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