Abstract
We construct a ‘structure invariant’ of a oneended, finitely presented group that describes the way in which the factors of its JSJ decomposition over twoended subgroups fit together. For hyperbolic groups satisfying a very general condition, these invariants completely reduce the problem of classifying such groups up to quasiisometry to a relative quasiisometry classification of the factors of their JSJ decomposition. Under some additional assumption, our results extend to more general finitely presented groups, yielding a farreaching generalisation of the quasiisometry classification of some 3–manifolds obtained by Behrstock and Neumann.
The same approach also allows us to obtain such a reduction for the problem of determining when two hyperbolic groups have homeomorphic Gromov boundaries.
The same approach also allows us to obtain such a reduction for the problem of determining when two hyperbolic groups have homeomorphic Gromov boundaries.
Original language  English 

Pages (fromto)  249291 
Number of pages  43 
Journal  Mathematical Proceedings of the Cambridge Philosophical Society 
Volume  162 
Issue number  2 
Early online date  30 Jun 2016 
DOIs  
Publication status  Published  Mar 2017 
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Alexandre Martin
 School of Mathematical & Computer Sciences  Associate Professor
 School of Mathematical & Computer Sciences, Mathematics  Associate Professor
Person: Academic (Research & Teaching)