欧几里得建筑的粗等价
度量几何
2013-12-10 v5 群论
摘要
我们证明了以下刚性结果。欧几里得建筑之间的粗等价保持无穷远处的球面建筑。如果所有不可约因子维数至少为2，则粗等价的欧几里得建筑是等距的（直至缩放因子）。如果此外没有不可约因子是欧几里得锥，则等距是唯一的，且与粗等价有有限距离。
引用
@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}
}
备注
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