Dehn functions of coabelian subgroups of direct products of groups
@inproceedings{Kropholler2021DehnFO, title={Dehn functions of coabelian subgroups of direct products of groups}, author={Robert P. Kropholler and Claudio Llosa Isenrich}, year={2021} }
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 onto a free abelian group. These improve and generalise previous results by Carter and Forester on Dehn functions of level sets in products of simply connected cube complexes, by Bridson on Dehn functions of cocyclic groups and by Dison on Dehn functions of coabelian groups. We then provide several…
References
SHOWING 1-10 OF 29 REFERENCES
The Dehn functions of Stallings–Bieri groups
- Mathematics
- 2015
We show that the Stallings–Bieri groups, along with certain other Bestvina–Brady groups, have quadratic Dehn function.
On the subgroups of semihyperbolic groups
- Essays on geometry and related topics, Vol. 1, 2, Monogr. Enseign. Math., vol. 38, Enseignement Math., Geneva
- 2001
A subgroup of a direct product of free groups whose Dehn function has a cubic lower bound
- Mathematics
- 2007
Abstract We establish a cubic lower bound on the Dehn function of a certain finitely presented subgroup of a direct product of three free groups.
Residually free groups do not admit a uniform polynomial isoperimetric function
- MathematicsProceedings of the American Mathematical Society
- 2020
We show that there is no uniform polynomial isoperimetric function for finitely presented subgroups of direct products of free groups, by producing a sequence of subgroups $G_r\leq F_2^{(1)} \times…
Identifying Dehn functions of Bestvina–Brady groups from their defining graphs
- Mathematics
- 2021
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…
Homological Dehn functions of groups of type $FP_2$.
- Mathematics
- 2020
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…
Cone-equivalent nilpotent groups with different Dehn functions
- Mathematics
- 2020
For every $k\geqslant 3$, we exhibit a simply connected $k$-nilpotent Lie group $N_k$ whose Dehn function behaves like $n^k$, while the Dehn function of its associated Carnot graded group behaves…
A FINITELY PRESENTED GROUP WHOSE 3-DIMENSIONAL INTEGRAL HOMOLOGY IS NOT FINITELY GENERArED.*
- Mathematics
- 1963
Doubles, Finiteness Properties of Groups, and Quadratic Isoperimetric Inequalities☆☆☆
- Mathematics
- 1999
Abstract We describe a doubling construction that gives many new examples of groups that satisfy a quadratic isoperimetric inequality. Using this construction, we prove that the presence of a…