Computations regarding the torsion homology of Oeljeklaus-Toma manifolds
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909831806320640 |
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| author | Phan, Dung Phuong Bui, Tuan Anh Rahm, Alexander D. |
| author_facet | Phan, Dung Phuong Bui, Tuan Anh Rahm, Alexander D. |
| contents | This article investigates the torsion homology behaviour in towers of Oeljeklaus-Toma (OT) manifolds. This adapts an idea of Silver and Williams from knot theory to OT-manifolds and extends it to higher degree homology groups. In the case of surfaces, i.e. Inoue surfaces of type $S^0$, the torsion grows exponentially in both $H_1$ (as was established by Braunling) and $H_2$ (our result) according to a parameter which already plays a role in Inoue's classical paper, and we obtain that the torsion vanishes in all higher degrees. This motivates our presented machine calculations for OT-manifolds of higher dimension. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2406_14942 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Computations regarding the torsion homology of Oeljeklaus-Toma manifolds Phan, Dung Phuong Bui, Tuan Anh Rahm, Alexander D. Differential Geometry K-Theory and Homology This article investigates the torsion homology behaviour in towers of Oeljeklaus-Toma (OT) manifolds. This adapts an idea of Silver and Williams from knot theory to OT-manifolds and extends it to higher degree homology groups. In the case of surfaces, i.e. Inoue surfaces of type $S^0$, the torsion grows exponentially in both $H_1$ (as was established by Braunling) and $H_2$ (our result) according to a parameter which already plays a role in Inoue's classical paper, and we obtain that the torsion vanishes in all higher degrees. This motivates our presented machine calculations for OT-manifolds of higher dimension. |
| title | Computations regarding the torsion homology of Oeljeklaus-Toma manifolds |
| topic | Differential Geometry K-Theory and Homology |
| url | https://arxiv.org/abs/2406.14942 |