Homological Dehn functions of groups of type $F{P}_2$

Abstract

We prove foundational results for homological Dehn functions of groups of type $F{P}_2$ 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 $F{P}_2$ with quartic homological Dehn function and unsolvable word problem.

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

Cited by in corpus (1)

• Dehn functions of coabelian subgroups of direct products of groups