# Homological Dehn functions of groups of type $FP_2$.

@article{Brady2020HomologicalDF, title={Homological Dehn functions of groups of type \$FP\_2\$.}, author={Noel Brady and Robert P. Kropholler and Ignat Soroko}, journal={arXiv: Group Theory}, year={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 Leary's groups $G_L(S)$ providing methods to obtain uncountably many groups with a given homological Dehn function. This allows us to show that there exist groups of type $FP_2$ with quartic homological Dehn function and unsolvable word problem.

## 2 Citations

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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…

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We construct 4–dimensional CAT(0) groups containing finitely presented subgroups whose Dehn functions are exp(x) for integers n,m ≥ 1 and 6–dimensional CAT(0) groups containing finitely presented…

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