Bi-Lipschitz embeddings of trees into Euclidean buildings (Q1421756)
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scientific article; zbMATH DE number 2037044
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Bi-Lipschitz embeddings of trees into Euclidean buildings |
scientific article; zbMATH DE number 2037044 |
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Bi-Lipschitz embeddings of trees into Euclidean buildings (English)
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3 February 2004
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Let \(B\) be the affine Bruhat-Tits building (also called Euclidean building) associated to a semisimple, simply connected linear algebraic group over a non-archimedean local field. In this paper the author proves that there exist locally finite trees of degree 3 which are bi-Lipschitz embedded in \(B\). As a consequence such a Euclidean building cannot be bi-Lipschitz embedded into a Hilbert space.
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bi-Lipschitz embeddings
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Bruhat-Tits buildings
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\(p\)-adic Lie group
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singular spaces of nonpositive curvature
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trees
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0.93712604
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0.9060036
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0.90464884
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0.8887502
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0.88759327
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0.88629013
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0.8818892
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0.8775022
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