Coarse equivalences of Euclidean buildings

We prove the following rigidity results. Coarse equivalences between metrically complete 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 add...

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Bibliographic Details
Published in:Advances in mathematics (New York. 1965) 2014-03, Vol.253, p.1-49
Main Authors: Kramer, Linus, Weiss, Richard M.
Format: Article
Language:English
Subjects:
Bruhat–Tits buildings
Euclidean buildings
Metric geometry
Quasi-isometric rigidity
Trees
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Summary:We prove the following rigidity results. Coarse equivalences between metrically complete 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. Appendix A shows how these results can be extended to non-complete Euclidean buildings.
ISSN:0001-8708
1090-2082
DOI:10.1016/j.aim.2013.10.031