圆柱树与正则分裂
Trees of cylinders and canonical splittings
摘要：
设T是一棵树，其作用为有限生成群G.给定T的边稳定子集合上的一个合适的等价关系（如可交换性、相对双曲群中的余元性或交换传递群中的可交换性），我们定义了一棵圆柱树T_c。这棵树只依赖于T的变形空间;特别地，如果T是JSJ分裂，它在G的自同构下是不变的。因此我们得到Out（G）-不变的循环或阿贝尔JSJ分裂。此外，T_c具有很强的相容性（如果两棵树有一个共同的加细，则它们是相容的）。
英文摘要：
Let T be a tree with an action of a finitely generated group G. Given a suitable equivalence relation on the set of edge stabilizers of T (such as commensurability, co-elementarity in a relatively hyperbolic group, or commutation in a commutative transitive group), we define a tree of cylinders T_c. This tree only depends on the deformation space of T; in particular, it is invariant under automorphisms of G if T is a JSJ splitting. We thus obtain Out(G)-invariant cyclic or abelian JSJ splittings. Furthermore, T_c has very strong compatibility properties (two trees are compatible if they have a common refinement).
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
