Lifting group actions, equivariant towers and subgroups of non-positively curved groups
Lifting group actions, equivariant towers and subgroups of non-positively curved groups
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提升群作用、等变塔和非正曲群的子群
DOI：
10.2140/agt.2014.14.2783
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发表时间：
2013
影响因子：
0.7
通讯作者：
Eduardo Martínez
中科院分区：
文献类型：
--
作者：
Richard Gaelan Hanlon;Eduardo Martínez
如果C是一类在取满子复盖下闭的复合体，G是一类在C中的单连通复盖上允许固有紧作用的群，则G在取有限表示子群下闭。因此，在取有限表示的子群时，下列类群是封闭的：几何作用于3维的正则CAT.0/简单复合体的群，k - 6的收缩群，以及几何作用于2维负弯曲复合体的群。我们还证明了有限非正弯曲立方3 -复形不等价于有限非正弯曲正则简单3 -复形的同伦。我们包括应用于相对双曲群和图解可约群。主要结果是通过发展等变塔的概念获得的，这是一个独立的兴趣。
If C is a class of complexes closed under taking full subcomplexes and covers and G is the class of groups admitting proper and cocompact actions on one-connected complexes in C , then G is closed under taking finitely presented subgroups. As a consequence the following classes of groups are closed under taking finitely presented subgroups: groups acting geometrically on regular CAT.0/ simplicial complexes of dimension 3, k‐systolic groups for k 6, and groups acting geometrically on 2‐dimensional negatively curved complexes. We also show that there is a finite non-positively curved cubical 3‐complex that is not homotopy equivalent to a finite non-positively curved regular simplicial 3‐complex. We include applications to relatively hyperbolic groups and diagrammatically reducible groups. The main result is obtained by developing a notion of equivariant towers, which is of independent interest.