Related papers: Polynomially-bounded Dehn functions of groups

We consider space functions $s(n)$ of finitely presented groups $G =< A\mid R> .$ (These functions have a natural geometric analog.) To define $s(n)$ we start with a word $w$ over $A$ of length at most $n$ equal to 1 in $G$ and use…

We introduce the class of perturbed right-angled Artin groups. These are constructed by gluing Bieri double groups into standard right-angled Artin groups. As a first application of this construction we obtain families of CAT(0) groups…

It is shown that there exist infinitely many non-integers $r>2$ such that the Dehn function of some finitely presented group is $\simeq n^r$. For each positive rational number $s$ we construct pairs of finitely presented groups $H\subset G$…

Given a finitely presented group $G$ and a surjective homomorphism $G\to \mathbb{Z}^n$ with finitely presented kernel $K$, we give an upper bound on the Dehn function of $K$ in terms of an area-radius pair for $G$. As a consequence we…

We construct examples of finitely generated decidable group presentations that satisfy certain combinations of solvability for the word problem, solvability for the bounded word problem, and computablity for the Dehn function. We prove that…

We show the connection between the relative Dehn function of a finitely generated metabelian group and the distortion function of a corresponding subgroup in the wreath product of two free abelian groups of finite rank. Further, we show…

We construct 4-dimensional CAT(0) groups containing finitely presented subgroups whose Dehn functions are $\exp^{(n)}(x^m)$ for integers $n, m \geq 1$ and 6-dimensional CAT(0) groups containing finitely presented subgroups whose Dehn…

We prove that the Bridson-Dison group has quartic Dehn function, thereby providing the first precise computation of the Dehn function of a subgroup of a direct product of free groups with super-quadratic Dehn function. We also prove that…

Gromov conjectured that any irreducible lattice in a symmetric space of rank at least 3 should have at most polynomial Dehn function. We prove that the lattice Sp(2p;Z) has quadratic Dehn function when p is at least 5. By results of…

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…

In 1999 Brady constructed the first example of a non-hyperbolic finitely presented subgroup of a hyperbolic group by fibring a non-positively curved cube complex over the circle. We show that his example has Dehn function bounded above by…

We prove foundational results for homological Dehn functions of groups of type $FP_2$ such as superadditivity and the invariance under quasi-isometry. We then study the homological Dehn functions of Leary's groups $G_L(S)$ providing methods…

We establish the existence, finiteness, and uniqueness up to scaling of various isoperimetric profiles of a group, in all dimensions. We also show that these profiles all coincide in dimensions 4 and higher; in particular, the nth Dehn…

We establish a cubic lower bound on the Dehn function of a certain finitely presented subgroup of a direct product of 3 free groups.

We prove that Abels' group over an arbitrary nondiscrete locally compact field has a quadratic Dehn function. As applications, we exhibit connected Lie groups and polycyclic groups whose asymptotic cones have uncountable abelian fundamental…

The Dehn function measures the area of minimal discs that fill closed curves in a space; it is an important invariant in analysis, geometry, and geometric group theory. There are several equivalent ways to define the Dehn function, varying…

We prove that when n >= 5, the Dehn function of SL(n;Z) is quadratic. The proof involves decomposing a disc in SL(n;R)/SO(n) into triangles of varying sizes. By mapping these triangles into SL(n;Z) and replacing large elementary matrices by…

We construct examples of finitely presented simple groups whose Dehn functions are at least exponential. To the best of our knowledge, these are the first such examples known. Our examples arise from R\"over-Nekrashevych groups, using…

We show that the Dehn function of the handlebody group is exponential in any genus $g\geq 3$. On the other hand, we show that the handlebody group of genus $2$ is cubical, biautomatic, and therefore has a quadratic Dehn function.

We construct the first examples of an algorithmically complex finitely presented residually finite groups and first examples of finitely presented residually finite groups with arbitrarily large (recursive) Dehn function and depth function.…