Splittings of finitely generated groups over two-ended subgroups (Q2759055)

The main results of the paper are versions of the annulus theorem and the JSJ splitting (from the theory of 3-manifolds) for one-ended, finitely generated groups over two-ended subgroups, starting with a finite collection of codimension-one two-ended subgroups. ``In the case of finitely presented groups, stronger results have been obtained by different methods by \textit{M. J. Dunwoody} and \textit{M. E. Sageev} [Invent. Math. 135, No. 1, 25-44 (1999; Zbl 0939.20047)] and Fujiwara-Papasoglu. The methods in the present paper differ in that they all apply directly to the finitely generated case, and that the splittings obtained are more canonical.'' In this theory, virtual surface groups play a central role, and so therefore do methods for recognizing them. Some of the previous work rests ultimately on the characterization of Fuchsian groups as convergence groups acting on the circle, which completed the proof of the Seifert conjecture. In the present paper another criterion is given, obtaining a characterization of a virtual surface group as one-ended finitely generated group which contains an infinite order element and such that every infinite order element is codimension-one.