Related papers: Big mapping class groups are not acylindrically hy…

The aim of this note is to give the simplest possible proof that Mapping Class Groups of closed hyperbolic surfaces are acylindrically hyperbolic, and more specifically that their curve graphs are hyperbolic and that pseudo-Anosovs act on…

We give a dynamical characterization of acylindrically hyperbolic groups. As an application, we prove that non-elementary convergence groups are acylindrically hyperbolic.

By recognizing them as fundamental groups of developable complexes of groups we prove that mapping class groups of compact orientable surfaces have finite asymptotic dimension.

We show that the verbal width is infinite for acylindrically hyperbolic groups, which include hyperbolic groups, mapping class groups and Out(Fn).

We proved that non-elementary discrete convergence groups are acylindrically hyperbolic.

Let $G$ be a finitely presented group, and let $H$ be a subgroup of $G$. We prove that if $H$ is acylindrically hyperbolic and existentially closed in $G$, then $G$ is acylindrically hyperbolic. As a corollary, any finitely presented group…

This paper completely determines the non-amenability of the mapping class groups of infinite-type surfaces, the mapping class groups of locally finite infinite graphs of higher ranks, gives an example of non-amenable stabiliser of a point…

We show that the pure mapping class group is uniformly perfect for a certain class of infinite type surfaces with noncompact boundary components. We then combine this result with recent work in the remaining cases to give a complete…

We prove that acylindrically hyperbolic groups are monotileable. That is, every finite subset of the group is contained in a finite tile. This provides many new examples of monotileable groups, and progress on the question of whether every…

We give a combinatorial criterion that implies both the non-strong relative hyperbolicity and the one-endedness of a finitely generated group. We use this to show that many important classes of groups do not admit a strong relatively…

Big mapping class groups are the mapping class groups of infinite-type surfaces, that is, surfaces whose fundamental groups are not finitely generated. While mapping class groups of finite-type surfaces have been extensively studied, the…

Even though big mapping class groups are not countably generated, certain big mapping class groups can be generated by a coarsely bounded set and have a well defined quasi-isometry type. We show that the big mapping class group of a stable…

We survey recent developments on mapping class groups of surfaces of infinite topological type.

By considering appropriate finite covering spaces of closed non-orientable surfaces, we construct linear representations of their mapping class group which have finite index image in certain big arithmetic groups.

We address the question of determining which mapping class groups of infinite-type surfaces admit nonelementary continuous actions on hyperbolic spaces. More precisely, let $\Sigma$ be a connected, orientable surface of infinite type with…

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…

Assuming that every hyperbolic group is residually finite, we prove the congruence subgroup property for mapping class groups of hyperbolic surfaces of finite type. Under the same assumption, it follows that profinitely equivalent…

This is an announcement of some of the results obtained as a part of the second author's Ph.D. thesis. In the first part, we prove that the fundamental group of an acylindrical complex of hyperbolic groups with finite edge groups is…

We use fine curve graph tools to prove that there exist parabolic isometries of graphs of curves associated to surfaces of infinite type.

We show that the automorphism groups of right-angled Artin groups whose defining graphs have at least 3 vertices are not relatively hyperbolic. We then show that the outer automorphism groups are not relatively hyperbolic, if they are not…