Boundaries and JSJ Decompositions of CAT(0)-Groups
نویسندگان
چکیده
منابع مشابه
Jsj-decompositions of Finitely Presented Groups and Complexes of Groups
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 ...
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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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The idea of “JSJ-decompositions” for 3-manifolds began with work of Waldhausen and was developed later through work of Jaco, Shalen and Johansen. It was shown that there is a finite collection of 2-sided, incompressible tori that separate a closed irreducible 3-manifold into pieces with strong topological structure. Sela introduced the idea of JSJ-decompositions for groups, an idea that has flo...
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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 decompositi...
متن کاملJSJ-DECOMPOSITIONS OF FINITELY PRESENTED GROUPS AND COMPLEXES OF GROUPS K. Fujiwara and P. Papasoglu
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...
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ژورنال
عنوان ژورنال: Geometric and Functional Analysis
سال: 2009
ISSN: 1016-443X,1420-8970
DOI: 10.1007/s00039-009-0012-8