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arXiv · 2012.00730

Homological Dehn functions of groups of type $FP_2$

Noel Brady·Robert Kropholler·Ignat Soroko
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Abstract

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.

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Noel Brady, Robert Kropholler, Ignat Soroko. 2020-12-01. Homological Dehn functions of groups of type $FP_2$. https://arxiv.org/abs/2012.00730

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