Anti-trees and right-angled Artin subgroups of braid groups
Anti-trees and right-angled Artin subgroups of braid groups
复制标题
辫子群的反树和直角Artin亚群
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
T. Koberda
中科院分区：
文献类型：
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作者：
Sang;T. Koberda
我们证明任意直角 Artin 群 G 允许准等距群嵌入到由树的相反图定义的直角 Artin 群中，从而嵌入到纯辫子群中。由此可见，G 是 2-盘和 2-球的保面积微分同胚群的准等距嵌入子群，具有适合 p 的 L p 度量。另一个推论是，每个维度都存在一个闭双曲流形群，它允许一个准等距群嵌入到一个纯辫子群中。最后，我们证明同构问题、共轭问题和隶属问题在辫群的有限表示子群类中是不可解的。
We prove that an arbitrary right-angled Artin group G admits a quasi-isometric group embedding into a right-angled Artin group defined by the opposite graph of a tree, and, consequently, into a pure braid group. It follows that G is a quasi-isometrically embedded subgroup of the area-preserving diffeomorphism groups of the 2‐disk and of the 2‐sphere with L p ‐metrics for suitable p . Another corollary is that there exists a closed hyperbolic manifold group of each dimension which admits a quasi-isometric group embedding into a pure braid group. Finally, we show that the isomorphism problem, conjugacy problem, and membership problem are unsolvable in the class of finitely presented subgroups of braid groups.