Effective JSJ Decompositions
نویسندگان
چکیده
In this paper we describe an elimination process which is a deterministic rewriting procedure that on each elementary step transforms one system of equations over free groups into a finitely many new ones. Infinite branches of this process correspond to cyclic splittings of the coordinate group of the initial system of equations. This allows us to construct algorithmically Grushko’s decompositions of finitely generated fully residually free groups and cyclic [abelian] JSJ decompositions of freely indecomposable finitely generated fully residually free groups. We apply these results to obtain an effective description of the set of homomorphisms from a given finitely presented group into a free group, or, more generally, into an NTQ group.
منابع مشابه
On uniqueness of JSJ decompositions of finitely generated groups
We show that JSJ decompositions of finitely generated groups are unique whenever they are strongly slide–free. When this condition does not hold they are still unique up to elementary deformation. These results hold for the decompositions of Rips and Sela, Dunwoody and Sageev, and Fujiwara and Papasoglu. We also answer the question of Rips and Sela stated in “Cyclic splittings of finitely prese...
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