# Dehn functions of subgroups of right-angled Artin groups

@article{Brady2018DehnFO,
title={Dehn functions of subgroups of right-angled Artin groups},
journal={Geometriae Dedicata},
year={2018},
volume={200},
pages={197-239}
}
• Published 12 September 2017
• Mathematics
• Geometriae Dedicata
We show that for each positive integer k there exist right-angled Artin groups containing free-by-cyclic subgroups whose monodromy automorphisms grow as $$n^k$$nk. As a consequence we produce examples of right-angled Artin groups containing finitely presented subgroups whose Dehn functions grow as $$n^{k+2}$$nk+2.
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## References

SHOWING 1-10 OF 44 REFERENCES

### On the Subgroups of Right Angled Artin Groups and Mapping Class Groups

There exist right angled Artin groups $A$ such that the isomorphism problem for finitely presented subgroups of $A$ is unsolvable, and for certain finitely presented subgroups the conjugacy and

### Minimal dimension faithful linear representations of common finitely presented groups

For various finitely presented groups, including right angled Artin groups and free by cyclic groups, we investigate what is the smallest dimension of a faithful linear representation. This is done

### Morse theory and finiteness properties of groups

• Mathematics
• 1997
Abstract. We examine the finiteness properties of certain subgroups of “right angled” Artin groups. In particular, we find an example of a group that is of type FP(Z) but is not finitely presented.

### Detecting the growth of free group automorphisms by their action on the homology of subgroups of finite index

We prove that if F is a finitely generated free group and f:F -> F is an automorphism with polynomial growth of degree d, then there exists a characteristic subgroup S < F of finite index such that

### Isoperimetric inequalities for the fundamental groups of torus bundles over the circle

• Mathematics
• 1994
We give upper bounds for isoperimetric functions of semi-direct products in terms of the asymptotic behaviour of ||Ak|| ask → ∞. In the caseA ∈ Sp(n, ℤ) we show that these bounds are sharp. This

### Free by cyclic groups and linear groups with restricted unipotent elements

• J. Button
• Mathematics
Groups Complex. Cryptol.
• 2017
It is shown that groups in this class of linear groups that do not contain unipotent elements of infinite order have good closure properties, in addition to having properties akin to non-positive curvature, which were proved in [6].

### Cubulating hyperbolic free-by-cyclic groups: The irreducible case

• Mathematics
• 2016
Let $V$ be a finite graph and let $\phi:V\rightarrow V$ be an irreducible train track map whose mapping torus has word-hyperbolic fundamental group $G$. Then $G$ acts freely and cocompactly on a

### An isoperimetric function for Bestvina–Brady groups

Given a right‐angled Artin group A, the associated Bestvina–Brady group is defined to be the kernel of the homomorphism A → ℤ that maps each generator in the standard presentation of A to a fixed

### Cubular tubular groups

. Let G split as a ﬁnite graph of free abelian groups with cyclic edge groups. We characterize when G acts freely on a CAT(0) cube complex. We show that if G acts properly and semi-simply on a CAT(0)

### Cubulating hyperbolic free-by-cyclic groups: the general case

• Mathematics
• 2014
Let $${\Phi\colon F\rightarrow F}$$Φ:F→F be an automorphism of the finite-rank free group F. Suppose that $${G=F\rtimes_\Phi\mathbb{Z}}$$G=F⋊ΦZ is word-hyperbolic. Then G acts freely and cocompactly