Torsion homology growth of polynomially growing free-by-cyclic groups
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866913646825701376 |
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| author | Andrew, Naomi Hughes, Sam Kudlinska, Monika |
| author_facet | Andrew, Naomi Hughes, Sam Kudlinska, Monika |
| contents | We show that the homology torsion growth of a free-by-cyclic group with polynomially growing monodromy vanishes in every dimension independently of the choice of Farber chain. It follows that the integral torsion $ρ^\mathbb{Z}$ equals the $\ell^2$-torsion $ρ^{(2)}$ verifying a conjecture of Lück for these groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_04389 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Torsion homology growth of polynomially growing free-by-cyclic groups Andrew, Naomi Hughes, Sam Kudlinska, Monika Group Theory Geometric Topology 20J05 (Primary) 20E05, 20E08, 20E26, 20F28, 57M07 (Secondary) We show that the homology torsion growth of a free-by-cyclic group with polynomially growing monodromy vanishes in every dimension independently of the choice of Farber chain. It follows that the integral torsion $ρ^\mathbb{Z}$ equals the $\ell^2$-torsion $ρ^{(2)}$ verifying a conjecture of Lück for these groups. |
| title | Torsion homology growth of polynomially growing free-by-cyclic groups |
| topic | Group Theory Geometric Topology 20J05 (Primary) 20E05, 20E08, 20E26, 20F28, 57M07 (Secondary) |
| url | https://arxiv.org/abs/2211.04389 |