Original Paper

Geometric & Functional Analysis GAFA

, Volume 16, Issue 1, pp 70-125

JSJ-Decompositions of finitely presented groups and complexes of groups

  • K. FujiwaraAffiliated withMathematical Institute, Tohoku University Email author 
  • , P. PapasogluAffiliated withMathematics Department, University of Athens

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Abstract.

A JSJ-splitting of a group G over a certain class of subgroups is a graph of groups decomposition of G which describes all possible decompositions of G as an amalgamated product or an HNN extension over subgroups lying in the given class. Such decompositions originated in 3-manifold topology. In this paper we generalize the JSJ-splitting constructions of Sela, Rips–Sela and Dunwoody–Sageev, and we construct a JSJ-splitting for any finitely presented group with respect to the class of all slender subgroups along which the group splits. Our approach relies on Haefliger’s theory of group actions on CAT(0) spaces.

Keywords and phrases.

JSJ-decomposition Complex of groups Bass–Serre theory

Mathematics Subject Classification (1991).

20F65 20E08 57M07