arXiv subjects

Adrien Abgrall

Publications and source records attributed to Adrien Abgrall.

3 recordsLinked to original sources

arXiv2025

Relative Untwisted Outer Space for Right-Angled Artin Groups

For G, H two finite collections of finitely generated subgroups of a right-angled Artin group A, the untwisted McCool group U(A; G, Ht) is the subgroup of untwisted outer automorphisms of A preserving the conjugacy class of each element of G and acting trivially up to conjugacy on each element of H. We prove that when the elements of G are standard subgroups of A, U(A; G, Ht) acts properly cocompactly on a finite-dimensional subcomplex of the spine of untwisted outer space for A, providing a geometric model for this group and proof that it is of type VF.

math.GR↗

arXiv2024

Spatial Cube Complexes

We provide a new geometric characterization for the spine of untwisted outer space of a right-angled Artin group, constructed by Charney, Stambaugh, and Vogtmann. We realize the spine as the natural simplicial complex associated with the category of spatial cube complexes, a new class of locally CAT(0) cube complexes with a simple definition in terms of hyperplane collapses.

math.GR↗

arXiv2024

On residual finiteness of graphs of free groups with cyclic edge groups

We characterize which groups splitting as finite graphs of free groups with cyclic edge groups are residually finite. Such a group $G$ is residually finite if and only if all its Baumslag-Solitar subgroups are residually finite. From a presentation of $G$, we construct a finite labeled graph $\Gamma$, and show that residual finiteness of $G$ is equivalent to an easily-detectable property of this graph. This characterization proves a conjecture of Wise.

math.GR↗