Virtual homological torsion: abundance versus growth in books of $I$-bundles
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866916971673550848 |
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| author | Fruchter, Jonathan |
| author_facet | Fruchter, Jonathan |
| contents | Let $\mathcal{B}$ be a book of $I$-bundles, all of whose pages are surfaces of negative Euler characteristic. In this short note, we prove that torsion in the first homology of $\mathcal{B}$ grows subexponentially in the index along any exhausting tower of regular finite-sheeted covers. By contrast, recent work of Ascari and the author shows that, apart from the obvious exceptions, $\mathcal{B}$ has abundant virtual homological torsion, which can grow exponentially along exhausting towers of non-regular finite covers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_22052 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Virtual homological torsion: abundance versus growth in books of $I$-bundles Fruchter, Jonathan Geometric Topology Group Theory 57M10, 20F65, 57M07 Let $\mathcal{B}$ be a book of $I$-bundles, all of whose pages are surfaces of negative Euler characteristic. In this short note, we prove that torsion in the first homology of $\mathcal{B}$ grows subexponentially in the index along any exhausting tower of regular finite-sheeted covers. By contrast, recent work of Ascari and the author shows that, apart from the obvious exceptions, $\mathcal{B}$ has abundant virtual homological torsion, which can grow exponentially along exhausting towers of non-regular finite covers. |
| title | Virtual homological torsion: abundance versus growth in books of $I$-bundles |
| topic | Geometric Topology Group Theory 57M10, 20F65, 57M07 |
| url | https://arxiv.org/abs/2509.22052 |