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Giovanni Sartori

Publications and source records attributed to Giovanni Sartori.

6 recordsLinked to original sources
arXiv2026

JSJ splittings for all Artin groups

We prove that an Artin group splits over infinite cyclic subgroups if and only if its defining graph has a separating vertex, and explicitly construct a JSJ decomposition over infinite cyclic subgroups for all Artin groups. We then use these facts to show that, if two Artin groups are isomorphic, then they have the same set of parabolics supported on "big chunks", that is, maximal subgraphs without separating vertices. We also deduce acylindrical hyperbolicity for the automorphism groups of many Artin groups, partially answering a question of Genevois in the case of Artin groups. As a consequence, we produce new families of Artin groups with the R-infinity property.

math.GR↗
arXiv2026

Parabolic subgroups of Dyer groups

For all Dyer groups, we find an algorithm to determine when two parabolic subgroups are conjugate. Given two conjugate standard parabolic subgroup, we fully describe the conjugating elements in terms of ribbons, showing that the ribbon conjecture holds true. In particular we give a description of the normaliser of a parabolic subgroup using ribbons. We prove the standardisation property for parabolic subgroups and deduce that an arbitrary intersection of parabolic subgroups is a parabolic subgroup.

math.GR↗
arXiv2026

A combination theorem for the twist conjecture for Artin groups

We reduce a strong version of the twist conjecture for Artin groups to Artin groups whose defining graphs have no separating vertices. This produces new examples of Artin groups satisfying the conjecture, and sheds more light on the isomorphism problem for Artin groups. Along the way we also prove a combination result for the ribbon property for vertices.

math.GR↗
arXiv2026

Isomorphism invariance of the girth of Artin groups

For all Artin groups, we characterise the girth (i.e. the length of a shortest cycle) of the defining graph algebraically, showing that it is an isomorphism invariant. Using this result, we prove that the Artin groups based on a cycle graph are isomorphically rigid. Alongside the girth, we introduce a new graph invariant, the weighted girth, which takes into account the labels of the defining graph. Within the class of two-dimensional Artin groups of hyperbolic type, we characterise the weighted girth in terms of certain minimal right-angled Artin subgroups, showing that it is an isomorphism invariant. Finally, under the further hypothesis of leafless defining graph, we recover the weighted girth as the girth of the commutation graph introduced by Hagen-Martin-Sisto.

math.GR↗
arXiv2025

Combination theorems for Wise's power alternative

We show that Wise's power alternative is stable under certain group constructions, use this to prove the power alternative for new classes of groups, and recover known results from a unified perspective. For groups acting on trees, we introduce a dynamical condition that allows us to deduce the power alternative for the group from the power alternative for its stabilisers of points. As an application, we reduce the power alternative for Artin groups to the power alternative for free-of-infinity Artin groups, under some conditions on their parabolic subgroups. We also introduce a uniform version of the power alternative and prove it, among other things, for a large family of two-dimensional Artin groups. As a corollary, we deduce that these Artin groups have uniform exponential growth. Finally, we prove that the power alternative is stable under taking relatively hyperbolic groups. We apply this to show that various examples, including all free-by-$\mathbb{Z}$ groups and a natural subclass of hierarchically hyperbolic groups, satisfy the uniform power alternative.

math.GR↗