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Acylindrical hyperbolicity and the centers of Artin groups that are not free of infinity
Motoko Kato, Shin-ichi Oguni
Charney and Morris-Wright showed acylindrical hyperbolicity of Artin groups of infinite type associated with graphs that are not joins, by studying clique-cube complexes and the ac…
Acylindrical hyperbolicity of Artin-Tits groups associated to triangle-free graphs and cones over square-free bipartite graphs
Motoko Kato, Shin-ichi Oguni
It is conjectured that the central quotient of every irreducible Artin group is either virtually cyclic or acylindrically hyperbolic. We prove this conjecture for Artin groups asso…
On relative hyperbolicity for a group and relative quasiconvexity for a subgroup
Yoshifumi Matsuda, Shin-ichi Oguni, Saeko Yamagata
We consider two families of subgroups of a group. Each subgroup which belongs to one family is contained in some subgroup which belongs to the other family. We then discuss relatio…
Notes on relatively hyperbolic groups and relatively quasiconvex subgroups
Yoshifumi Matsuda, Shin-ichi Oguni, Saeko Yamagata
We define relatively quasiconvex subgroups of relatively hyperbolic groups in the sense of Osin and show that such subgroups have expected properties. Also we state several definit…