A cutpoint tree for a continuum (Q2702058)

A result on continua (compact connected Hausdorff spaces) is proved which simplifies the proof of the cut point conjecture for negatively curved groups (i.e. that the continuum \(X=\partial G\), for a negatively curved group \(G\), has no cut points). For the proof of the cut point conjecture, assuming the presence of cut points, a suitable action of \(G\) on an \(\mathbb{R}\)-tree is constructed and then led to a contradiction. In the present paper, the construction of a tree is achieved by associating to a Hausdorff continuum \(X\) and a set of cut points \(C\) of \(X\) a ``tree'' \(T\supset C\) and a relation between \(X\) and \(T\) which preserves the seperation properties of \(C\).NEWLINENEWLINEFor the entire collection see [Zbl 0940.00028].