A Geometric Proof of Stallings' Theorem on Groups with More than One End
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Stallings showed that a finitely generated group which has more than one end splits as an amalgamated free product or an HNN extension over a finite subgroup. Dunwoody gave a new geometric proof of the theorem for the class of almost finitely presented groups, and separately, using somewhat different methods, generalised it to a larger class of splittings. Here we adapt the geometric method to the class of finitely generated groups using Sageev's generalisation of Bass Serre theory concerning group pairs with more than one end, and show that this new proof simultaneously establishes Dunwoody's generalisation.
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- 1.Bridson, M. R. and Haefliger, A.: Metric Spaces of Non-positive Curvature, Springer-Verlag, Berlin, 1999.Google Scholar
- 3.Dicks, W. and Dunwoody, M. J.: Groups Acting on Graphs, Cambridge University Press, 1989.Google Scholar
- 17.Serre, J. P.: Trees, Translated from the French by John Stillwell, Springer-Verlag, Berlin, 1980.Google Scholar
- 19.Stallings, J. R.: Group Theory and 3-Dimensional Manifolds, Yale Math. Monogr. 4, Yale University Press, New Haven, 1971.Google Scholar