Homological Dehn functions of groups of type $FP_2$
Group Theory
2021-07-13 v3 Geometric Topology
Abstract
We prove foundational results for homological Dehn functions of groups of type such as superadditivity and the invariance under quasi-isometry. We then study the homological Dehn functions of Leary's groups providing methods to obtain uncountably many groups with a given homological Dehn function. This allows us to show that there exist groups of type with quartic homological Dehn function and unsolvable word problem.
Keywords
Cite
@article{arxiv.2012.00730,
title = {Homological Dehn functions of groups of type $FP_2$},
author = {Noel Brady and Robert Kropholler and Ignat Soroko},
journal= {arXiv preprint arXiv:2012.00730},
year = {2021}
}
Comments
v3: Updates to section 7: answered question 7.13 affirmatively, shorter proof of Th. 7.3 added, minor improvements throughout; v2: Section 2 reorganized, one figure and few references added, minor changes throughout. 44 pages, 5 figures