Identifying Dehn functions of Bestvina–Brady groups from their defining graphs

@article{Chang2021IdentifyingDF,
  title={Identifying Dehn functions of Bestvina–Brady groups from their defining graphs},
  author={Yu-Chan Chang},
  journal={Geometriae Dedicata},
  year={2021},
  pages={1-29}
}
  • Yu-Chan Chang
  • Published 5 March 2021
  • Mathematics
  • Geometriae Dedicata
Let $$\Gamma $$ be a finite simplicial graph such that the flag complex on $$\Gamma $$ is a 2-dimensional triangulated disk. We show that with some assumptions, the Dehn function of the associated Bestvina–Brady group is either quadratic, cubic, or quartic. Furthermore, we can identify the Dehn function from the defining graph $$\Gamma $$ . 
Dehn functions of coabelian subgroups of direct products of groups
We develop new methods for computing the precise Dehn functions of coabelian subgroups of direct products of groups, that is, subgroups which arise as kernels of homomorphisms from the direct product

References

SHOWING 1-10 OF 14 REFERENCES
Metric Spaces of Non-Positive Curvature
This book describes the global properties of simply-connected spaces that are non-positively curved in the sense of A. D. Alexandrov, and the structure of groups which act on such spaces by
Morse theory and finiteness properties of groups
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.
Dehn functions of subgroups of right-angled Artin groups
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
The Dehn functions of Stallings–Bieri groups
We show that the Stallings–Bieri groups, along with certain other Bestvina–Brady groups, have quadratic Dehn function.
Snowflake geometry in CAT (0) groups
We construct CAT (0) groups containing subgroups whose Dehn functions are given by xs , for a dense set of numbers s∈[2,∞) . This significantly expands the known geometric behavior of subgroups of
On Dehn functions and products of groups
If G is a finitely presented group then its Dehn function ― or its isoperimetric inequality ― is of interest. For example, G satisfies a linear isoperimetric inequality iff G is negatively curved (or
An introduction to right-angled Artin groups
Recently, right-angled Artin groups have attracted much attention in geometric group theory. They have a rich structure of subgroups and nice algorithmic properties, and they give rise to cubical
...
...