Dehn functions of subgroups of products of free groups. Part II: Precise computations
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909478389022720 |
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| author | Ascari, Dario Bertolotti, Federica Italiano, Giovanni Isenrich, Claudio Llosa Migliorini, Matteo |
| author_facet | Ascari, Dario Bertolotti, Federica Italiano, Giovanni Isenrich, Claudio Llosa Migliorini, Matteo |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_03180 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dehn functions of subgroups of products of free groups. Part II: Precise computations Ascari, Dario Bertolotti, Federica Italiano, Giovanni Isenrich, Claudio Llosa Migliorini, Matteo Group Theory Geometric Topology 20F65 (Primary) 20F05, 20F67, 20F69, 57M07 (Secondary) 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. |
| title | Dehn functions of subgroups of products of free groups. Part II: Precise computations |
| topic | Group Theory Geometric Topology 20F65 (Primary) 20F05, 20F67, 20F69, 57M07 (Secondary) |
| url | https://arxiv.org/abs/2502.03180 |