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A Geometric Proof of Stallings' Theorem on Groups with More than One End
 Graham A. Niblo
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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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 Title
 A Geometric Proof of Stallings' Theorem on Groups with More than One End
 Journal

Geometriae Dedicata
Volume 105, Issue 1 , pp 6176
 Cover Date
 20040401
 DOI
 10.1023/B:GEOM.0000024780.73453.e4
 Print ISSN
 00465755
 Online ISSN
 15729168
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 amalgamated free product
 Bassâ€“Serre theory
 CAT(0) cube complex
 ends
 HNN extension
 singularity obstruction
 Stallings' theorem
 Industry Sectors
 Authors

 Graham A. Niblo ^{(1)}
 Author Affiliations

 1. Faculty of Mathematical Studies, University of Southampton, Highfield, Southampton, SO17 1BJ, U.K.