Related papers: Abelian Splittings and JSJ-Decompositions of Bestv…
We give a combinatorial criterion for determining which Bestvina--Brady group is isomorphic to a right-angled Artin group.
We characterize when (and how) a Right-Angled Artin group splits nontrivially over an abelian subgroup.
Bestvina-Brady groups arise as kernels of length homomorphisms from right-angled Artin groups G_\G to the integers. Under some connectivity assumptions on the flag complex \Delta_\G, we compute several algebraic invariants of such a group…
We show that the Stallings-Bieri groups, along with certain other Bestvina-Brady groups, have quadratic Dehn function.
We classify abelian subgroups of two-dimensional Artin groups.
A JSJ-splitting of a group $G$ over a certain class of subgroups is a graph of groups decomposition of $G$ which describes all possible decompositions of $G$ as an amalgamated product or an HNN extension over subgroups lying in the given…
We develop JSJ decomposition theory of pro-p groups.
Right-angled Artin groups and their subgroups are of great interest because of their geometric, combinatorial and algorithmic properties. It is convenient to define these groups using finite simplicial graphs. The isomorphism type of the…
A group G is a vGBS group if it admits a decomposition as a finite graph of groups with all edge and vertex groups finitely generated and free abelian. We construct the JSJ decomposition of a vGBS group over abelian groups. We prove that…
This paper is the second in a series of two papers which study the phenomenon of tropical split Jacobians. The first paper is a contemplative study, embedded in the broader context of exploring connections between the category of tropical…
We prove that the Dehn function of every finitely presented Bestvina-Brady group grows as a linear, quadratic, cubic, or quartic polynomial. In fact, we provide explicit criteria on the defining graph to determine the degree of this…
A JSJ decomposition of a group is a splitting that allows one to classify all possible splittings of the group over a certain family of edge groups. Although JSJ decompositions are not unique in general, Guirardel--Levitt have constructed a…
We show that quasi-projective Bestvina-Brady groups are fundamental groups of complements to hyperplane arrangements. Furthermore we relate other normal subgroups of right-angled Artin groups to complements to arrangements of hypersurfaces.…
The abstract will be added in due course.
The JSJ decomposition encodes the automorphisms and the virtually cyclic splittings of a hyperbolic group. For general finitely presented groups, the JSJ decomposition encodes only their splittings. In this sequence of papers we study the…
We survey the problem of separation under conjugacy and malnormality of the abelian peripheral subgroups of an orientable, irreducible $3$-manifold $X$. We shall focus on the relation between this problem and the existence of acylindrical…
Analogues of JSJ decompositions were developed for Poincar\'e duality pairs in [19]. These decompositions depend only on the group. Our focus will be on describing the edge splittings of these decompositions more precisely. We use our…
We exhibit free-by-cyclic groups containing non-free locally-free subgroups, including some word hyperbolic examples. We also show that these groups are not subgroup separable. We use Bestvina-Brady Morse theory in our arguments.
We classify all possible JSJ decompositions of doubles of free groups of rank two and we then compute the Makanin-Razborov diagram of a particular double of a free group and deduce that in general limit groups are not freely subgroup…
For each subcomplex of the standard CW-structure on any torus, we compute the homology of a certain infinite cyclic regular covering space. In all cases when the homology is finitely generated, we also compute the cohomology ring. For…