Hyperbolically embedded subgroups and rotating families in groups acting on hyperbolic spaces
نویسندگان
چکیده
منابع مشابه
Indecomposable Groups Acting on Hyperbolic Spaces
We obtain a number of finiteness results for groups acting on hy-perbolic spaces and R-trees. In particular we show that a torsion-free locally quasiconvex hyperbolic group has only finitely many conjugacy classes of n-generated one-ended subgroups. We also prove an acylindrical accessibility theorem for groups acting on R-trees.
متن کاملTrain tracks and surface groups acting on hyperbolic spaces
Let Σ be a compact surface, and letM be a path metric space with π1(M) ∼= π1(Σ) and with the universal cover M̃ Gromov hyperbolic. We show that, under certain assumptions, the shortest realisation in M of a multicurve Σ can be approximated by a train track in M . In the case where M is a hyperbolic 3-manifold, this is well known (see for example [Bon]). The main result is stated as Theorem 0.1 h...
متن کاملNielsen Methods and Groups Acting on Hyperbolic Spaces
We show that for any n ∈ N there exists a constant C(n) such that any n-generated group G which acts by isometries on a δ-hyperbolic space (with δ > 0) is either free or has a nontrivial element with translation length at most δC(n).
متن کاملSome Remarks on Subgroups of Hyperbolic Groups
If G is a hyperbolic group, where G = H oφ Z, H is finitely presented, and φ is an automorphism of H, then H satisfies a polynomial isoperimetric inequality. Necessary and sufficient conditions of homological character are given for a finitely presented subgroup H of a hyperbolic group to be hyperbolic (resp. a quasi-convex subgroup). If Y is a connected subcomplex of the finite connected 2comp...
متن کاملQuasiconvex Subgroups and Nets in Hyperbolic Groups
Consider a hyperbolic group G and a quasiconvex subgroup H ⊂ G with [G : H] = ∞. We construct a set-theoretic section s : G/H → G of the quotient map (of sets) G → G/H such that s(G/H) is a net in G; that is, any element of G is a bounded distance from s(G/H). This section arises naturally as a set of points minimizing word-length in each fixed coset gH. The left action of G on G/H induces an a...
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: Memoirs of the American Mathematical Society
سال: 2017
ISSN: 0065-9266,1947-6221
DOI: 10.1090/memo/1156