منابع مشابه
Submultiplicativity and the Hanna Neumann Conjecture
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...
متن کاملA Proof of the Strengthened Hanna Neumann Conjecture
We prove the Strengthened Hanna Neumann Conjecture. We give a more direct cohomological interpretation of the conjecture in terms of “typical” covering maps, and use graph Galois theory to “symmetrize” the conjecture. The conjecture is then related to certain kernel of a morphism of sheaves, and is implied provided these kernels are co-acyclic in the covering cohomology theory. This allows us t...
متن کاملThe Topology and Analysis of the Hanna Neumann Conjecture
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...
متن کاملJoel Friedman’s proof of the strengthened Hanna Neumann conjecture
1.1 Notation. As Bourbaki intended, we let N denote the set of finite cardinals, {0, 1, 2, . . .}. Throughout this section, let F be a field. We shall write dim(V ) to denote the F-dimension of an F-module V . Throughout this section, let (Z,VZ,EZ,EZ ι,τ −→ VZ) be a finite (oriented) graph; here, Z is a finite set, VZ ⊆ Z, EZ = Z −VZ, and ι and τ are functions. Each e ∈ EZ has an associated pic...
متن کاملGraphs, 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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ژورنال
عنوان ژورنال: Proceedings of the Glasgow Mathematical Association
سال: 1956
ISSN: 2040-6185,2051-2104
DOI: 10.1017/s2040618500033384