Dehn functions of subgroups of products of free groups. Part II: Precise computations

• DOI: 10.48550/arxiv.2502.03180
• Publication Date: 2025-01-01
• Authors: Ascari, Dario; Bertolotti, Federica; Italiano, Giovanni; Isenrich, Claudio...; Migliorini, Matteo
• Keywords: Mathematics - Geometric Topology; 20F65 (Primary) 20F05, 20F67, 20F69, 57M07 (Secondary); FOS: Mathematics; Geometric Topology (math.GT); Group Theory (math.GR); Mathematics - Group Theory

The paper arXiv:2406.19860v1 was split into two parts. This is the second part (Theorem B and E of the original version). The first part is available at arXiv:2406.19860v2. 27 pages, 3 figures<br/>We prove that the Bridson-Dison group has quartic Dehn function, thereby providing the first precise computation of the Dehn function of a subgroup of a direct product of free groups with super-quadratic Dehn function. We also prove that coabelian subgroups of direct products of $n$ free groups of finiteness type $\mathcal{F}_{n-1}$ and of corank $r\leq n-2$ have quadratic Dehn functions.<br/>