论文标题
方面delaGéométriedes groupes
Aspects de la géométrie des groupes
论文作者
论文摘要
这本《 Habilitation Memoir》（法语，2014年5月提交）由五章组成，每章都是在2006年至2014年之间作者的作品的介绍。回忆录的核心是前三章，与几何小组理论有关。更确切地说，它与群体，尤其是谎言组的大规模几何形状（第1章和第2章）以及局部紧凑的双曲线群有关（第3章）。第4章通过其单一表示及其对希尔伯特空间（Kazhdan和Haagerup属性）的等轴测行为的研究关注。最后，第5章更关注“结构”群体理论，研究给定的组（离散或更通常是局部紧凑），其封闭子组的空间或封闭的正常亚组。附加了一个公开问题的列表。虽然回忆录大部分是发表论文，但它还在第1章中介绍了一些未发表的推论，内容涉及说谎组的渐近锥。
This habilitation memoir (in French, submitted in May 2014) is made up of five chapters, each being an introduction to work of the author between 2006 and 2014. The core of the memoir consists of the first three chapters, pertaining to geometric group theory. More precisely, it is concerned with large-scale geometry of groups and especially Lie groups (Chapters 1 and 2), and locally compact hyperbolic groups (Chapter 3). Chapter 4 is concerned with the study of groups through their unitary representations and their isometric actions on Hilbert spaces (Kazhdan and Haagerup properties). Finally, Chapter 5 is more concerned with "structural" group theory, studying, for a given group (discrete, or more generally locally compact), the space of its closed subgroups, or closed normal subgroups. A list of open questions is appended. While the memoir mostly surveys published papers, it also presents some unpublished corollaries in Chapter 1 about asymptotic cones of Lie groups.
