发表机构
Unité de Mathématiques Pures et Appliquées, UMR 5669 CNRS, École normale supérieure de Lyon（纯数学与应用数学单位，CNRS联合研究单位5669，里昂高等师范学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究探讨李群渐近锥的基本群，证明含SOL型商群的李群的渐近锥基本群包含夏威夷耳环基本群，还获其一阶同调群非零结果，依托前人成果明确SOL障碍的几何等价条件。
AI 中文摘要
我们研究李群的渐近锥，建立了权的几何与渐近锥高度非单连通性质之间的联系。我们证明，若一个李群以SOL型群为商群，则其渐近锥的基本群包含夏威夷耳环空间的基本群。我们还得到了渐近锥一阶同调群的强非零结果。该李群的这一假设由阿贝尔斯（Abels）提出，称为“SOL障碍”，它等价于权上的显式几何条件。我们的工作基于布里略（Burillo）的成果，布里illo证明了SOL情形下渐近锥的相关结论；也基于科尔努利耶（Cornulier）和泰塞拉（Tessera）的成果，他们证明了SOL障碍会导致Dehn函数的指数增长。
英文摘要
We study asymptotic cones of Lie groups, presenting a link between the geometry of the weights and the highly non-simply-connected nature of asymptotic cones. We show that a Lie group that admits a group of SOL-type as a quotient is such that the fundamental group of its asymptotic cone contains the fundamental group of the Hawaiian earring space. We also obtain a strong non-vanishing result for the first homology group of the asymptotic cone. The assumption on the Lie group, introduced by Abels and called the "SOL obstruction", is equivalent to an explicit geometric condition on the weights. Our work builds upon the results of Burillo, who proves the statement on asymptotic cones in the case of SOL, and on those of Cornulier and Tessera who show that the SOL obstruction implies exponential growth of the Dehn function.
Comments43 pages, 8 figures
