Forking and JSJ decompositions in the free group
نویسندگان
چکیده
منابع مشابه
Forking in the free group
We study model-theoretic and stability-theoretic properties of the nonabelian free group in the light of Sela’s recent result [15] on stability and results announced by Bestvina and Feighn on “negligible subsets” of free groups. We point out analogies between the free group and socalled bad groups of finite Morley rank, and prove “non CM -triviality” of the free group.
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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...
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We study model-theoretic and stability-theoretic properties of the nonabelian free group in the light of Sela’s recent result [15] on stability and results announced by Bestvina and Feighn on “negligible subsets” of free groups. We point out analogies between the free group and socalled bad groups of finite Morley rank, and prove “non CM -triviality”
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This paper is a survey of some of the most elementary consequences of the JSJ-decomposition and geometrization for knot and link complements in S3 . Formulated in the language of graphs, the result is the construction of a bijective correspondence between the isotopy classes of links in S3 and a class of vertex-labelled, finite acyclic graphs, called companionship graphs. This construction can ...
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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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ژورنال
عنوان ژورنال: Journal of the European Mathematical Society
سال: 2016
ISSN: 1435-9855
DOI: 10.4171/jems/636