Adjunction inequalities and the Davis hyperbolic four-manifold
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916649937928192 |
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| author | Lin, Francesco Martelli, Bruno |
| author_facet | Lin, Francesco Martelli, Bruno |
| contents | The Davis hyperbolic four-manifold $\mathcal{D}$ is not almost-complex, so that its Seiberg-Witten invariants corresponding to zero-dimensional moduli spaces are vanishing by definition. In this paper, we show that all the Seiberg-Witten invariants involving higher-dimensional moduli spaces also vanish. Our proof involves the adjunction inequalities corresponding to 864 genus two totally geodesic surfaces embedded inside $\mathcal{D}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_08536 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Adjunction inequalities and the Davis hyperbolic four-manifold Lin, Francesco Martelli, Bruno Geometric Topology The Davis hyperbolic four-manifold $\mathcal{D}$ is not almost-complex, so that its Seiberg-Witten invariants corresponding to zero-dimensional moduli spaces are vanishing by definition. In this paper, we show that all the Seiberg-Witten invariants involving higher-dimensional moduli spaces also vanish. Our proof involves the adjunction inequalities corresponding to 864 genus two totally geodesic surfaces embedded inside $\mathcal{D}$. |
| title | Adjunction inequalities and the Davis hyperbolic four-manifold |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2503.08536 |