1999
DOI: 10.4310/mrl.1999.v6.n6.a9
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A small unstable action on a tree

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Cited by 6 publications
(7 citation statements)
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“…Suppose that one end of a foliated 2-cell is as in Fig 6 . Thus v is the end vertex of the 2-cell and adjacent vertices are x, y and x, y are mapped to the same point of T , so that they lie on the same vertical line. Let the adjacent 1-cells to v be e 1 and e 2 , which conflicts with our earlier notation but is in line with that of [7] and [2]. Let the groups associated with the cells (in the complex of groups) be denoted by the corresponding capital letters.…”
Section: Finitely Presented Groupsmentioning
confidence: 98%
See 1 more Smart Citation
“…Suppose that one end of a foliated 2-cell is as in Fig 6 . Thus v is the end vertex of the 2-cell and adjacent vertices are x, y and x, y are mapped to the same point of T , so that they lie on the same vertical line. Let the adjacent 1-cells to v be e 1 and e 2 , which conflicts with our earlier notation but is in line with that of [7] and [2]. Let the groups associated with the cells (in the complex of groups) be denoted by the corresponding capital letters.…”
Section: Finitely Presented Groupsmentioning
confidence: 98%
“…Folding the corner results in a fold of the graph of groups associated with the 1-skeleton of X. Such a fold is one of three types which are listed in [2] (as Type A folds) or in [7]. They are shown in Fig 8 for the reader's convenience.…”
Section: Finitely Presented Groupsmentioning
confidence: 99%
“…T is called stable if every nondegenerate arc J ⊂ T contains a stable subarc. M. Dunwoody [8] constructed example of a small but unstable action of a finitely generated group Γ on a tree. To remedy this, we introduce the following modification of stability, adapted to the case of actions whose image on Isom(T ) is small: Definition 6.2.…”
Section: Is Eventually Constant the Action γmentioning
confidence: 99%
“…In fact, Shalen [28] asked whether this is true in general, i.e., if every finitely generated group admitting a non-trivial action on an R-tree also admits a non-trivial action (without edge inversions) on some simplicial tree. A clear indication that the answer to this question should be negative was given by Dunwoody in [12], who constructed an example of a finitely generated group which has a non-trivial unstable action on some R-tree with finite cyclic arc stabilizers, but cannot act non-trivially on a simplicial tree with small edge stabilizers (although, as observed in [12], this group does possess a non-trivial action on some simplicial tree).…”
Section: Introductionmentioning
confidence: 99%