Coarse Equivalences of Euclidean Buildings
Metric Geometry
2013-12-10 v5 Group Theory
Abstract
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.
Cite
@article{arxiv.0902.1332,
title = {Coarse Equivalences of Euclidean Buildings},
author = {Linus Kramer and Richard M Weiss and Jeroen Schillewaert and Koen Struyve},
journal= {arXiv preprint arXiv:0902.1332},
year = {2013}
}
Comments
To appear in: Advances in Mathematics. v2: Substantially revised and expanded. v3: We have added an appendix by Jeroen Schillewaert and Koen Struyve which shows that our main results hold also for non-complete Euclidean buildings. v4 and v5: Some minor typos and misprints corrected