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 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.
متن کاملThe generic Hanna Neumann Conjecture and Post Correspondence Problem
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 the Australian Mathematical Society
سال: 1974
ISSN: 0004-9735
DOI: 10.1017/s1446788700015913