Essential tori associated with links of mixed singularities
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866915963102822400 |
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| author | Santos, Raimundo N. Araújo dos Bode, Benjamin de Paiva, Thiago Quiceno, Eder L. Sanchez |
| author_facet | Santos, Raimundo N. Araújo dos Bode, Benjamin de Paiva, Thiago Quiceno, Eder L. Sanchez |
| contents | We establish a direct connection between the analytic data of weakly isolated mixed singularities and the topology of their associated links. More precisely, we prove that the existence of essential tori, topological information, in the complements of links arising from weakly isolated mixed singularities can be detected directly from properties of the defining mixed polynomial, provided that it is convenient, non-degenerate and $Γ$-nice.
Our results provide explicit and computable criteria, expressed purely in terms of the polynomial data, that determine the presence of essential tori in the link exterior. In particular, these criteria yield effective conditions ensuring that such links are non-hyperbolic.
This approach provides a new method to extract topological information about link complements without requiring an explicit determination of the link type, thereby establishing a concrete bridge between the analytic structure of mixed polynomials and the geometric topology of their associated links. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_25517 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Essential tori associated with links of mixed singularities Santos, Raimundo N. Araújo dos Bode, Benjamin de Paiva, Thiago Quiceno, Eder L. Sanchez Geometric Topology Algebraic Geometry Primary 57K10 14P05, Secondary 14M25 57K31 14P25 We establish a direct connection between the analytic data of weakly isolated mixed singularities and the topology of their associated links. More precisely, we prove that the existence of essential tori, topological information, in the complements of links arising from weakly isolated mixed singularities can be detected directly from properties of the defining mixed polynomial, provided that it is convenient, non-degenerate and $Γ$-nice. Our results provide explicit and computable criteria, expressed purely in terms of the polynomial data, that determine the presence of essential tori in the link exterior. In particular, these criteria yield effective conditions ensuring that such links are non-hyperbolic. This approach provides a new method to extract topological information about link complements without requiring an explicit determination of the link type, thereby establishing a concrete bridge between the analytic structure of mixed polynomials and the geometric topology of their associated links. |
| title | Essential tori associated with links of mixed singularities |
| topic | Geometric Topology Algebraic Geometry Primary 57K10 14P05, Secondary 14M25 57K31 14P25 |
| url | https://arxiv.org/abs/2604.25517 |