On Finiteness of Homological Isoperimetric Functions on Top Dimensions
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866915806046060544 |
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| author | Martínez-Pedroza, Eduardo Torres, Diana Vizcaíno |
| author_facet | Martínez-Pedroza, Eduardo Torres, Diana Vizcaíno |
| contents | We address a question from \cite{BKV25} regarding the finiteness of the homological $R$-isoperimetric function. Let $R$ be a subfield of the complex numbers $\mathbb{C}$ with the absolute value norm. We prove that for any group $G$ that admits a finite $(n+1)$-dimensional model for $K(G,1)$, the homological $n$-isoperimetric function of $G$ over $R$ is either linear or takes infinite values. In particular, by results of Gersten and Mineyev, in the class of groups admitting a finite $2$-dimensional classifying space, the homological $1$-dimensional isoperimetric function over $R$ only captures hyperbolicity. This follows as a particular case of a more general result proved in this note. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_16881 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On Finiteness of Homological Isoperimetric Functions on Top Dimensions Martínez-Pedroza, Eduardo Torres, Diana Vizcaíno Group Theory We address a question from \cite{BKV25} regarding the finiteness of the homological $R$-isoperimetric function. Let $R$ be a subfield of the complex numbers $\mathbb{C}$ with the absolute value norm. We prove that for any group $G$ that admits a finite $(n+1)$-dimensional model for $K(G,1)$, the homological $n$-isoperimetric function of $G$ over $R$ is either linear or takes infinite values. In particular, by results of Gersten and Mineyev, in the class of groups admitting a finite $2$-dimensional classifying space, the homological $1$-dimensional isoperimetric function over $R$ only captures hyperbolicity. This follows as a particular case of a more general result proved in this note. |
| title | On Finiteness of Homological Isoperimetric Functions on Top Dimensions |
| topic | Group Theory |
| url | https://arxiv.org/abs/2602.16881 |