Geometriae Dedicata

, Volume 105, Issue 1, pp 61–76

A Geometric Proof of Stallings' Theorem on Groups with More than One End

  • Graham A. Niblo

DOI: 10.1023/B:GEOM.0000024780.73453.e4

Cite this article as:
Niblo, G.A. Geometriae Dedicata (2004) 105: 61. doi:10.1023/B:GEOM.0000024780.73453.e4


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.

amalgamated free productBass–Serre theoryCAT(0) cube complexendsHNN extensionsingularity obstructionStallings' theorem

Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Graham A. Niblo
    • 1
  1. 1.Faculty of Mathematical StudiesUniversity of SouthamptonHighfield, SouthamptonU.K.