Coarse Equivalences of Euclidean Buildings

Jeroen Schillewaert; Koen Struyve; Linus Kramer; Richard M Weiss

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Coarse Equivalences of Euclidean Buildings

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arxiv 0902.1332 v5 pith:GWTSHPZQ submitted 2009-02-08 math.MG math.GR

Linus Kramer , Richard M Weiss , Jeroen Schillewaert , Koen Struyve This is my paper

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keywords buildingseuclideancoarsefactorsequivalencesirreduciblethenaddition

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We prove the following rigidity results. Coarse equivalences between Euclidean buildings preserve spherical buildings at infinity. If all irreducible factors have dimension at least two, then coarsely equivalent Euclidean buildings are isometric (up to scaling factors). If in addition none of the irreducible factors is a Euclidean cone, then the isometry is unique and has finite distance from the coarse equivalence.

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