Wirtinger curves, Artin groups, and hypocycloids
| Autor: | José Ignacio Cogolludo-Agustín, Jorge Martín-Morales, Enrique Artal Bartolo |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Computer Science::Machine Learning
Fundamental group Pure mathematics Plane curve Computation 01 natural sciences Mathematics - Algebraic Geometry Mathematics - Geometric Topology Wirtinger presentation FOS: Mathematics 0101 mathematics Algebraic number Algebraic Geometry (math.AG) Mathematics Complement (set theory) Algebra and Number Theory Group (mathematics) Applied Mathematics 010102 general mathematics Geometric Topology (math.GT) 010101 applied mathematics Computational Mathematics Family of curves 14H30 57M10 32S05 20F36 14H50 Geometry and Topology Analysis |
| Zdroj: | Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas. 112:641-656 |
| ISSN: | 1579-1505 1578-7303 |
| DOI: | 10.1007/s13398-017-0437-0 |
| Popis: | The computation of the fundamental group of the complement of an algebraic plane curve has been theoretically solved since Zariski-van Kampen, but actual computations are usually cumbersome. In this work, we describe the notion of Wirtinger presentation of such a group relying on the real picture of the curve and with the same combinatorial flavor as the classical Wirtinger presentation; we determine a significant family of curves for which Wirtinger presentation provides the required fundamental group. The above methods allow us to compute that fundamental group for an infinite subfamily of hypocycloids, relating them with Artin groups. Comment: 16 pages, 8 figures, to appear in Revista de la Real Academia de Ciencias Exactas, F\'isicas y Naturales. Serie A. Matem\'aticas |
| Databáze: | OpenAIRE |
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