Links of singularities of inner non-degenerate mixed functions
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866909498022559744 |
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| author | Santos, Raimundo N. Araújo dos Bode, Benjamin Quiceno, Eder L. Sanchez |
| author_facet | Santos, Raimundo N. Araújo dos Bode, Benjamin Quiceno, Eder L. Sanchez |
| contents | We introduce the notion of a (strongly) inner non-degenerate mixed function $f:\mathbb{C}^2\to\mathbb{C}$. We show that inner non-degenerate mixed polynomials have weakly isolated singularities and strongly inner non-degenerate mixed polynomials have isolated singularities. Furthermore, under one additional assumption, which we call "niceness", the links of these singularities can be completely characterized in terms of the Newton boundary of $f$. In particular, adding terms above the Newton boundary does not affect the topology of the link. This allows us to define an infinite family of real algebraic links in the 3-sphere. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2208_11655 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Links of singularities of inner non-degenerate mixed functions Santos, Raimundo N. Araújo dos Bode, Benjamin Quiceno, Eder L. Sanchez Geometric Topology Primary 32S55, 57K10, Secondary 14M25, 14P05, 14P15, 14P25, 32S05 We introduce the notion of a (strongly) inner non-degenerate mixed function $f:\mathbb{C}^2\to\mathbb{C}$. We show that inner non-degenerate mixed polynomials have weakly isolated singularities and strongly inner non-degenerate mixed polynomials have isolated singularities. Furthermore, under one additional assumption, which we call "niceness", the links of these singularities can be completely characterized in terms of the Newton boundary of $f$. In particular, adding terms above the Newton boundary does not affect the topology of the link. This allows us to define an infinite family of real algebraic links in the 3-sphere. |
| title | Links of singularities of inner non-degenerate mixed functions |
| topic | Geometric Topology Primary 32S55, 57K10, Secondary 14M25, 14P05, 14P15, 14P25, 32S05 |
| url | https://arxiv.org/abs/2208.11655 |