On the growth of torsion in the cohomology of some arithmetic groups of $\mathbb{Q}$-rank one
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866917274859864064 |
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| author | Mueller, Werner Rochon, Frédéric |
| author_facet | Mueller, Werner Rochon, Frédéric |
| contents | Given a number field $F$ with ring of integers $\mathcal{O}_{F}$, one can associate to any torsion free subgroup of $\operatorname{SL}(2,\mathcal{O}_{F})$ of finite index a complete Riemannian manifold of finite volume with fibered cusp ends. For natural choices of flat vector bundles on such a manifold, we show that analytic torsion is identified with the Reidemeister torsion of the Borel-Serre compactification. This is used to obtain exponential growth of torsion in the cohomology for sequences of congruence subgroups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_14205 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the growth of torsion in the cohomology of some arithmetic groups of $\mathbb{Q}$-rank one Mueller, Werner Rochon, Frédéric Differential Geometry Geometric Topology Number Theory 58J52, 53C35, 55N25 Given a number field $F$ with ring of integers $\mathcal{O}_{F}$, one can associate to any torsion free subgroup of $\operatorname{SL}(2,\mathcal{O}_{F})$ of finite index a complete Riemannian manifold of finite volume with fibered cusp ends. For natural choices of flat vector bundles on such a manifold, we show that analytic torsion is identified with the Reidemeister torsion of the Borel-Serre compactification. This is used to obtain exponential growth of torsion in the cohomology for sequences of congruence subgroups. |
| title | On the growth of torsion in the cohomology of some arithmetic groups of $\mathbb{Q}$-rank one |
| topic | Differential Geometry Geometric Topology Number Theory 58J52, 53C35, 55N25 |
| url | https://arxiv.org/abs/2401.14205 |