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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.00177 |
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| _version_ | 1866916695507992576 |
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| author | Howladar, Satyanath |
| author_facet | Howladar, Satyanath |
| contents | We show that Baumslag-Solitar groups are virtually 2-avoidable, that is, they admit finite index subgroup whose first homology is devoid of $\mathbb{Z}_2$ summand. We also prove virtual 2-avoidability for some other classes of one-relator groups, which generalizes non-orientable surface groups. This along with result from a previous paper confirms Gromov's Conjecture about macroscopic dimension of universal cover of PSC manifolds, for all closed oriented spin manifolds whose fundamental group is product of Baumslag-Solitar groups, the one-relator groups under consideration. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_00177 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Gromov's Conjecture for Product of Baumslag-Solitar groups and some other One-relator groups Howladar, Satyanath Group Theory We show that Baumslag-Solitar groups are virtually 2-avoidable, that is, they admit finite index subgroup whose first homology is devoid of $\mathbb{Z}_2$ summand. We also prove virtual 2-avoidability for some other classes of one-relator groups, which generalizes non-orientable surface groups. This along with result from a previous paper confirms Gromov's Conjecture about macroscopic dimension of universal cover of PSC manifolds, for all closed oriented spin manifolds whose fundamental group is product of Baumslag-Solitar groups, the one-relator groups under consideration. |
| title | Gromov's Conjecture for Product of Baumslag-Solitar groups and some other One-relator groups |
| topic | Group Theory |
| url | https://arxiv.org/abs/2504.00177 |