An Analogue of the Strengthened Hanna Neumann Conjecture for Virtually Free Groups and Virtually Free Products
نویسندگان
چکیده
The Friedman--Mineyev theorem, earlier known as the (strengthened) Hanna Neumann conjecture, gives a sharp estimate for rank of intersection two subgroups in free group. We obtain an analogue this inequality any virtually group (or, more generally, containing product left-orderable groups finite-index subgroup).
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.
متن کاملA Characterisation of Virtually Free Groups
We prove that a finitely generated group G is virtually free if and only if there exists a generating set for G and k > 0 such that all k-locally geodesic words with respect to that generating set are geodesic.
متن کاملFurstenberg Entropy Realizations for Virtually Free Groups and Lamplighter Groups
Let (G, μ) be a discrete group with a generating probability measure. Nevo shows that if G has property (T) then there exists an ε > 0 such that the Furstenberg entropy of any (G, μ)-stationary space is either zero or larger than ε. Virtually free groups, such as SL2(Z), do not have property (T). For these groups, we construct stationary actions with arbitrarily small, positive entropy. This co...
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 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 کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Michigan Mathematical Journal
سال: 2023
ISSN: ['0026-2285', '1945-2365']
DOI: https://doi.org/10.1307/mmj/20216105