Computation-free presentation of the fundamental group of generic \((p,q)\)-torus curves (Q441072)
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scientific article; zbMATH DE number 6068596
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Computation-free presentation of the fundamental group of generic \((p,q)\)-torus curves |
scientific article; zbMATH DE number 6068596 |
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Computation-free presentation of the fundamental group of generic \((p,q)\)-torus curves (English)
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20 August 2012
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fundamental groups
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generic torus curves
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The paper gives a new method to compute fundamental groups of complements of complex projective plane curves using Nagata transformations and fibrations from ruled rational surfaces.NEWLINENEWLINEAs an application the authors obtain a quick proof that the fundamental group of a generic \((p,q)\)-torus knot is the direct product \(\mathbb{Z}/p\mathbb{Z} \times\mathbb{Z}/q\mathbb{Z}\).
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