Graphs, free groups and the Hanna Neumann conjecture
نویسندگان
چکیده
منابع مشابه
Graphs, free groups and the Hanna Neumann conjecture
A new bound for the rank of the intersection of finitely generated subgroups of a free group is given, formulated in topological terms, and in the spirit of Stallings [19]. The bound is a contribution to the strengthened Hanna Neumann conjecture.
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The relationship between free groups and graphs is one of the many examples of the interaction between seemingly foreign branches of mathematics. After defining and proving elementary relations between graphs and groups, this paper will present a result of Hanna Neumann on the intersection of free subgroups. Although Neumann’s orginal upper bound on the rank of the intersection has been improve...
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We define submultiplicativity of `-numbers in the category of Γ-complexes over a given Γ-complex X̂, which generalizes the statement of the Strengthened Hanna Neumann Conjecture (SHNC). In the case when Γ is a left-orderable group and X̂ is a free Γ-complex, we prove submultiplicativity for the subcategory consisting of Γ-ordered leafages over X̂ with an additional analytic assumption called the d...
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The statement of the Hanna Neumann Conjecture (HNC) is purely algebraic: for a free group Γ and any nontrivial finitely generated subgroups A and B of Γ, rk (A ∩B)− 1 ≤ (rkA− 1)(rkB − 1). The goal of this paper is to systematically develop machinery that would allow for generalizations of HNC and to exhibit their relations with topology and analysis. On the topological side we define immersions...
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Let F be a finitely generated free group, and K 6 F be a finitely generated, infinite index subgroup of F . We show that generically many finitely generated subgroups H 6 F have trivial intersection with all conjugates of K, thus proving a stronger, generic form of the Hanna Neumann Conjecture. As an application, we show that the equalizer of two free group homomorphisms is generically trivial,...
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ژورنال
عنوان ژورنال: Journal of Group Theory
سال: 2008
ISSN: 1433-5883,1435-4446
DOI: 10.1515/jgt.2008.057