Related papers: Hyperbolic groups that are not commensurably coHop…

Let S be a closed surface of genus at least 2. We show that a finitely generated group G which is an extension of the fundamental group H of S is word hyperbolic if and only the orbit map of the quotient group G/H on the complex of curves…

We show that in dimensions $>1$ the cohomology groups of the Higson compactification of the hyperbolic space $\H^n$ with respect to the $C_0$ coarse structure are trivial. Also we prove that the cohomology groups of the Higson…

We prove that every finitely generated soluble group which is not virtually abelian has a subgroup of one of a small number of types.

For a $k$-uniform hypergraph $\mathcal{H}$ on vertex set $\{1, ..., n\}$ we associate a particular signed incidence matrix $M(\mathcal{H})$ over the integers. For $\mathcal{H} \sim \mathcal{H}_k(n, p)$ an Erd\H{o}s--R\'{e}nyi random…

We introduce non-abelian cohomology sets of Hopf algebras with coefficients in Hopf modules. We prove that these sets generalize Serre's non-abelian group cohomology theory. Using descent techniques, we establish that our construction…

We construct a non-free but aleph_1-separable, torsion-free abelian group G with a pure free subgroup B such that all subgroups of G disjoint from B are free and such that G/B is divisible. This answers a question of Irwin and shows that a…

By defining the classes of generalized co-Hopfian and relatively co-Hopfian groups, respectively, we consider two expanded versions of the generalized co-Bassian groups and of the classical co-Hopfian groups giving a close relationship with…

We show that the presence of a non-contractible one-periodic orbit of a Hamiltonian diffeomorphism of a connected closed symplectic manifold $(M,\omega)$ implies the existence of infinitely many non-contractible simple periodic orbits,…

We study coarse separation in one-ended hyperbolic groups from a quantitative point of view, focusing on the volume growth of separating subsets. We prove that a one-ended hyperbolic group that is not virtually a surface group is coarsely…

We give a necessary and sufficient condition for the fundamental group of a finite graph of groups with infinite cyclic edge groups to be acylindrically hyperbolic, from which it follows that a finitely generated group splitting over Z…

We classify the boundaries of hyperbolic groups that have enough quasiconvex codimension-1 surface subgroups with trivial or cyclic intersections.

We determine the finite non-abelian simple groups which occur as the type of a Hopf-Galois structure on a solvable extension. In the language of skew braces, our result gives a complete list of finite non-abelian simple groups which occur…

We show that if $G$ is a non-elementary word hyperbolic group, mapping class group of a hyperbolic surface or the outer automorphism group of a nonabelian free group then $G$ has $2^{\aleph_0}$ many continuous ergodic invariant random…

A result of Gersten states that if $G$ is a hyperbolic group with integral cohomological dimension $\mathsf{cd}_{\mathbb{Z}}(G)=2$ then every finitely presented subgroup is hyperbolic. We generalize this result for the rational case…

We will show that, for any noncompact arithmetic hyperbolic $m$-manifold with $m> 3$, and any compact arithmetic hyperbolic $m$-manifold with $m> 4$ that is not a $7$-dimensional arithmetic hyperbolic manifold defined by octonions, its…

In 1995, Rips and Sela asked if torsionfree hyperbolic groups admit globally stable cylinders. We establish this property for all residually finite hyperbolic groups and curve graphs of finite-type surfaces. These cylinders are fine…

We prove that a uniformly coarsely proper hyperbolic cone over a bounded metric space consisting of a finite union of uniformly coarsely connected components each containing at least two points is non-amenable and apply this to visual…

We prove that every $C^2$ conservative partially hyperbolic diffeomorphism of a closed 3-manifold without periodic points is ergodic, which gives an affirmative answer to the Ergodicity Conjecture by Hertz-Hertz-Ures in the absence of…

A finitely generated subgroup H of a torsion-free hyperbolic group G is called immutable if there are only finitely many conjugacy classes of injections of H into G. We show that there is no uniform algorithm to recognize immutability,…

We construct uncountably many finitely generated, pairwise non-isomorphic torsion-free groups, all of which fall into the same quasi-isometry class. This is done by considering Schur covering groups and group cohomology, with the necessary…