Forester刚性结果的一个简短证明
A very short proof of Forester's rigidity result
摘要：
单纯G-树T的变形空间是由T通过某些收缩和扩张移动得到的G-树的集合，或者等价地，它们具有与T相同的椭圆子群。给出了Forester的一个刚性结果的一个简短证明，该结果给出了变形空间包含Aut（G）-不变G-树的一个充分条件.这给出了JSJ分裂在G的自同构下不变的一个充分条件。更准确地说，该定理声称变形空间最多包含一个强无滑G-树，其中强无滑意味着：只要两条边e_1，e_2入射到同一顶点v上，使得G_{e_1}是G_{e_2}的子集，则e_1和e_2在G_v下的同一轨道上。
英文摘要：
The deformation space of a simplicial G-tree T is the set of G-trees which can be obtained from T by some collapse and expansion moves, or equivalently, which have the same elliptic subgroups as T. We give a short proof of a rigidity result by Forester which gives a sufficient condition for a deformation space to contain an Aut(G)-invariant G-tree. This gives a sufficient condition for a JSJ splitting to be invariant under automorphisms of G. More precisely, the theorem claims that a deformation space contains at most one strongly slide-free G-tree, where strongly slide-free means the following: whenever two edges e_1, e_2 incident on a same vertex v are such that G_{e_1} is a subset of G_{e_2}, then e_1 and e_2 are in the same orbit under G_v.
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