Relatively dominated representations
Relatively dominated representations
复制标题
相对占主导地位的代表性
DOI：
10.5802/aif.3449
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发表时间：
2019
期刊：
影响因子：
--
通讯作者：
Fenglin Zhu
中科院分区：
文献类型：
--
作者：
Fenglin Zhu
阿诺索夫表示给出了一阶李群中凸协紧性的更高阶类似物，它具有许多良好的几何和动力学性质；第一级的几何有限性可以被视为凸协紧性的受控削弱，以允许双曲性的孤立失效。我们引入相对主导表示作为阿诺索夫表示的相对化，或者换句话说，几何有限性的更高阶类似物。我们证明，承认相对主导表示的群必定是相对双曲的，这些表示导出具有良好性质的极限图，提供示例，并与 Kapovich-Leeb 的工作建立联系，该工作还引入了几何有限性的更高阶类似物。
Anosov representations give a higher-rank analogue of convex cocompactness in a rank-one Lie group which shares many of its good geometric and dynamical properties; geometric finiteness in rank one may be seen as a controlled weakening of convex cocompactness to allow for isolated failures of hyperbolicity. We introduce relatively dominated representations as a relativization of Anosov representations, or in other words a higher-rank analogue of geometric finiteness. We prove that groups admitting relatively dominated representations must be relatively hyperbolic, that these representations induce limit maps with good properties, provide examples, and draw connections to work of Kapovich--Leeb which also introduces higher-rank analogues of geometric finiteness.